diff --git a/src/datasets/download/streaming_download_manager.py b/src/datasets/download/streaming_download_manager.py
index f0aa67dae73..697f5122b44 100644
--- a/src/datasets/download/streaming_download_manager.py
+++ b/src/datasets/download/streaming_download_manager.py
@@ -234,10 +234,14 @@ def xisfile(path, use_auth_token: Optional[Union[str, bool]] = None) -> bool:
     if is_local_path(main_hop):
         return os.path.isfile(path)
     else:
-        if rest_hops and fsspec.get_fs_token_paths(rest_hops[0])[0].protocol == "https":
-            storage_options = {
-                "https": {"headers": get_authentication_headers_for_url(rest_hops[0], use_auth_token=use_auth_token)}
-            }
+        if not rest_hops and (main_hop.startswith("http://") or main_hop.startswith("https://")):
+            main_hop, http_kwargs = _prepare_http_url_kwargs(main_hop, use_auth_token=use_auth_token)
+            storage_options = http_kwargs
+        elif rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
+            url = rest_hops[0]
+            url, http_kwargs = _prepare_http_url_kwargs(url, use_auth_token=use_auth_token)
+            storage_options = {"https": http_kwargs}
+            path = "::".join([main_hop, url, *rest_hops[1:]])
         else:
             storage_options = None
         fs, *_ = fsspec.get_fs_token_paths(path, storage_options=storage_options)
@@ -257,10 +261,14 @@ def xgetsize(path, use_auth_token: Optional[Union[str, bool]] = None) -> int:
     if is_local_path(main_hop):
         return os.path.getsize(path)
     else:
-        if rest_hops and fsspec.get_fs_token_paths(rest_hops[0])[0].protocol == "https":
-            storage_options = {
-                "https": {"headers": get_authentication_headers_for_url(rest_hops[0], use_auth_token=use_auth_token)}
-            }
+        if not rest_hops and (main_hop.startswith("http://") or main_hop.startswith("https://")):
+            main_hop, http_kwargs = _prepare_http_url_kwargs(main_hop, use_auth_token=use_auth_token)
+            storage_options = http_kwargs
+        elif rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
+            url = rest_hops[0]
+            url, http_kwargs = _prepare_http_url_kwargs(url, use_auth_token=use_auth_token)
+            storage_options = {"https": http_kwargs}
+            path = "::".join([main_hop, url, *rest_hops[1:]])
         else:
             storage_options = None
         fs, *_ = fsspec.get_fs_token_paths(path, storage_options=storage_options)
@@ -285,14 +293,20 @@ def xisdir(path, use_auth_token: Optional[Union[str, bool]] = None) -> bool:
     if is_local_path(main_hop):
         return os.path.isdir(path)
     else:
-        if rest_hops and fsspec.get_fs_token_paths(rest_hops[0])[0].protocol == "https":
-            storage_options = {
-                "https": {"headers": get_authentication_headers_for_url(rest_hops[0], use_auth_token=use_auth_token)}
-            }
+        if not rest_hops and (main_hop.startswith("http://") or main_hop.startswith("https://")):
+            raise NotImplementedError("os.path.isdir is not extended to support URLs in streaming mode")
+        elif rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
+            url = rest_hops[0]
+            url, http_kwargs = _prepare_http_url_kwargs(url, use_auth_token=use_auth_token)
+            storage_options = {"https": http_kwargs}
+            path = "::".join([main_hop, url, *rest_hops[1:]])
         else:
             storage_options = None
         fs, *_ = fsspec.get_fs_token_paths(path, storage_options=storage_options)
-        return fs.isdir(main_hop)
+        inner_path = main_hop.split("://")[1]
+        if not inner_path.strip("/"):
+            return True
+        return fs.isdir(inner_path)
 
 
 def xrelpath(path, start=None):
@@ -463,14 +477,20 @@ def xlistdir(path: str, use_auth_token: Optional[Union[str, bool]] = None) -> Li
         return os.listdir(path)
     else:
         # globbing inside a zip in a private repo requires authentication
-        if rest_hops and fsspec.get_fs_token_paths(rest_hops[0])[0].protocol == "https":
-            storage_options = {
-                "https": {"headers": get_authentication_headers_for_url(rest_hops[0], use_auth_token=use_auth_token)}
-            }
+        if not rest_hops and (main_hop.startswith("http://") or main_hop.startswith("https://")):
+            raise NotImplementedError("os.listdir is not extended to support URLs in streaming mode")
+        elif rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
+            url = rest_hops[0]
+            url, http_kwargs = _prepare_http_url_kwargs(url, use_auth_token=use_auth_token)
+            storage_options = {"https": http_kwargs}
+            path = "::".join([main_hop, url, *rest_hops[1:]])
         else:
             storage_options = None
         fs, *_ = fsspec.get_fs_token_paths(path, storage_options=storage_options)
-        objects = fs.listdir(main_hop.split("://")[1])
+        inner_path = main_hop.split("://")[1]
+        if inner_path.strip("/") and not fs.isdir(inner_path):
+            raise FileNotFoundError(f"Directory doesn't exist: {path}")
+        objects = fs.listdir(inner_path)
         return [os.path.basename(obj["name"]) for obj in objects]
 
 
@@ -490,7 +510,9 @@ def xglob(urlpath, *, recursive=False, use_auth_token: Optional[Union[str, bool]
         return glob.glob(main_hop, recursive=recursive)
     else:
         # globbing inside a zip in a private repo requires authentication
-        if rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
+        if not rest_hops and (main_hop.startswith("http://") or main_hop.startswith("https://")):
+            raise NotImplementedError("glob.glob is not extended to support URLs in streaming mode")
+        elif rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
             url = rest_hops[0]
             url, kwargs = _prepare_http_url_kwargs(url, use_auth_token=use_auth_token)
             storage_options = {"https": kwargs}
@@ -502,7 +524,8 @@ def xglob(urlpath, *, recursive=False, use_auth_token: Optional[Union[str, bool]
         #   so to be able to glob patterns like "[0-9]", we have to call `fs.glob`.
         # - Also "*" in get_fs_token_paths() only matches files: we have to call `fs.glob` to match directories.
         # - If there is "**" in the pattern, `fs.glob` must be called anyway.
-        globbed_paths = fs.glob(main_hop)
+        inner_path = main_hop.split("://")[1]
+        globbed_paths = fs.glob(inner_path)
         return ["::".join([f"{fs.protocol}://{globbed_path}"] + rest_hops) for globbed_path in globbed_paths]
 
 
@@ -522,7 +545,9 @@ def xwalk(urlpath, use_auth_token: Optional[Union[str, bool]] = None):
         yield from os.walk(main_hop)
     else:
         # walking inside a zip in a private repo requires authentication
-        if rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
+        if not rest_hops and (main_hop.startswith("http://") or main_hop.startswith("https://")):
+            raise NotImplementedError("os.walk is not extended to support URLs in streaming mode")
+        elif rest_hops and (rest_hops[0].startswith("http://") or rest_hops[0].startswith("https://")):
             url = rest_hops[0]
             url, kwargs = _prepare_http_url_kwargs(url, use_auth_token=use_auth_token)
             storage_options = {"https": kwargs}
@@ -530,7 +555,10 @@ def xwalk(urlpath, use_auth_token: Optional[Union[str, bool]] = None):
         else:
             storage_options = None
         fs, *_ = fsspec.get_fs_token_paths(urlpath, storage_options=storage_options)
-        for dirpath, dirnames, filenames in fs.walk(main_hop):
+        inner_path = main_hop.split("://")[1]
+        if inner_path.strip("/") and not fs.isdir(inner_path):
+            return []
+        for dirpath, dirnames, filenames in fs.walk(inner_path):
             yield "::".join([f"{fs.protocol}://{dirpath}"] + rest_hops), dirnames, filenames
 
 
diff --git a/tests/hub_fixtures.py b/tests/hub_fixtures.py
index 6bbc4f27e18..d710a410a44 100644
--- a/tests/hub_fixtures.py
+++ b/tests/hub_fixtures.py
@@ -60,13 +60,13 @@ def hf_private_dataset_repo_txt_data(hf_private_dataset_repo_txt_data_):
 
 
 @pytest.fixture(scope="session")
-def hf_private_dataset_repo_zipped_txt_data_(hf_api: HfApi, hf_token, zip_csv_path):
+def hf_private_dataset_repo_zipped_txt_data_(hf_api: HfApi, hf_token, zip_csv_with_dir_path):
     repo_name = f"repo_zipped_txt_data-{int(time.time() * 10e3)}"
     create_repo(hf_api, repo_name, token=hf_token, organization=USER, repo_type="dataset", private=True)
     repo_id = f"{USER}/{repo_name}"
     hf_api.upload_file(
         token=hf_token,
-        path_or_fileobj=str(zip_csv_path),
+        path_or_fileobj=str(zip_csv_with_dir_path),
         path_in_repo="data.zip",
         repo_id=repo_id,
         repo_type="dataset",
diff --git a/tests/test_streaming_download_manager.py b/tests/test_streaming_download_manager.py
index f57f5d47e3d..5da2298323a 100644
--- a/tests/test_streaming_download_manager.py
+++ b/tests/test_streaming_download_manager.py
@@ -23,8 +23,10 @@
     xrelpath,
     xsplit,
     xsplitext,
+    xwalk,
 )
 from datasets.filesystems import COMPRESSION_FILESYSTEMS
+from datasets.utils.file_utils import hf_hub_url
 
 from .utils import require_lz4, require_zstandard, slow
 
@@ -302,6 +304,16 @@ def test_xlistdir(input_path, expected_paths, tmp_path, mock_fsspec):
     assert output_paths == expected_paths
 
 
+def test_xlistdir_private(hf_private_dataset_repo_zipped_txt_data, hf_token):
+    root_url = hf_hub_url(hf_private_dataset_repo_zipped_txt_data, "data.zip")
+    assert len(xlistdir("zip://::" + root_url, use_auth_token=hf_token)) == 1
+    assert len(xlistdir("zip://main_dir::" + root_url, use_auth_token=hf_token)) == 2
+    with pytest.raises(FileNotFoundError):
+        xlistdir("zip://qwertyuiop::" + root_url, use_auth_token=hf_token)
+    with pytest.raises(NotImplementedError):
+        xlistdir(root_url, use_auth_token=hf_token)
+
+
 @pytest.mark.parametrize(
     "input_path, isdir",
     [
@@ -319,6 +331,15 @@ def test_xisdir(input_path, isdir, tmp_path, mock_fsspec):
     assert xisdir(input_path) == isdir
 
 
+def test_xisdir_private(hf_private_dataset_repo_zipped_txt_data, hf_token):
+    root_url = hf_hub_url(hf_private_dataset_repo_zipped_txt_data, "data.zip")
+    assert xisdir("zip://::" + root_url, use_auth_token=hf_token) is True
+    assert xisdir("zip://main_dir::" + root_url, use_auth_token=hf_token) is True
+    assert xisdir("zip://qwertyuiop::" + root_url, use_auth_token=hf_token) is False
+    with pytest.raises(NotImplementedError):
+        xisdir(root_url, use_auth_token=hf_token)
+
+
 @pytest.mark.parametrize(
     "input_path, isfile",
     [
@@ -335,6 +356,12 @@ def test_xisfile(input_path, isfile, tmp_path, mock_fsspec):
     assert xisfile(input_path) == isfile
 
 
+def test_xisfile_private(hf_private_dataset_repo_txt_data, hf_token):
+    root_url = hf_hub_url(hf_private_dataset_repo_txt_data, "")
+    assert xisfile(root_url + "data/text_data.txt", use_auth_token=hf_token) is True
+    assert xisfile(root_url + "qwertyuiop", use_auth_token=hf_token) is False
+
+
 @pytest.mark.parametrize(
     "input_path, size",
     [
@@ -351,6 +378,13 @@ def test_xgetsize(input_path, size, tmp_path, mock_fsspec):
     assert xgetsize(input_path) == size
 
 
+def test_xgetsize_private(hf_private_dataset_repo_txt_data, hf_token):
+    root_url = hf_hub_url(hf_private_dataset_repo_txt_data, "")
+    assert xgetsize(root_url + "data/text_data.txt", use_auth_token=hf_token) == 39
+    with pytest.raises(FileNotFoundError):
+        xgetsize(root_url + "qwertyuiop", use_auth_token=hf_token)
+
+
 @pytest.mark.parametrize(
     "input_path, expected_paths",
     [
@@ -386,6 +420,50 @@ def test_xglob(input_path, expected_paths, tmp_path, mock_fsspec):
     assert output_paths == expected_paths
 
 
+def test_xglob_private(hf_private_dataset_repo_zipped_txt_data, hf_token):
+    root_url = hf_hub_url(hf_private_dataset_repo_zipped_txt_data, "data.zip")
+    assert len(xglob("zip://**::" + root_url, use_auth_token=hf_token)) == 3
+    assert len(xglob("zip://qwertyuiop/*::" + root_url, use_auth_token=hf_token)) == 0
+
+
+@pytest.mark.parametrize(
+    "input_path, expected_outputs",
+    [
+        ("tmp_path", [("", [], ["file1.txt", "file2.txt", "README.md"])]),
+        (
+            "mock://top_level/second_level",
+            [
+                ("mock://top_level/second_level", ["date=2019-10-01", "date=2019-10-02", "date=2019-10-04"], []),
+                ("mock://top_level/second_level/date=2019-10-01", [], ["a.parquet", "b.parquet"]),
+                ("mock://top_level/second_level/date=2019-10-02", [], ["a.parquet"]),
+                ("mock://top_level/second_level/date=2019-10-04", [], ["a.parquet"]),
+            ],
+        ),
+    ],
+)
+def test_xwalk(input_path, expected_outputs, tmp_path, mock_fsspec):
+    if input_path.startswith("tmp_path"):
+        input_path = input_path.replace("/", os.sep).replace("tmp_path", str(tmp_path))
+        expected_outputs = sorted(
+            [
+                (str(tmp_path / dirpath).rstrip("/"), sorted(dirnames), sorted(filenames))
+                for dirpath, dirnames, filenames in expected_outputs
+            ]
+        )
+        for file in ["file1.txt", "file2.txt", "README.md"]:
+            (tmp_path / file).touch()
+    outputs = sorted(xwalk(input_path))
+    outputs = [(dirpath, sorted(dirnames), sorted(filenames)) for dirpath, dirnames, filenames in outputs]
+    assert outputs == expected_outputs
+
+
+def test_xwalk_private(hf_private_dataset_repo_zipped_txt_data, hf_token):
+    root_url = hf_hub_url(hf_private_dataset_repo_zipped_txt_data, "data.zip")
+    assert len(list(xwalk("zip://::" + root_url, use_auth_token=hf_token))) == 2
+    assert len(list(xwalk("zip://main_dir::" + root_url, use_auth_token=hf_token))) == 1
+    assert len(list(xwalk("zip://qwertyuiop::" + root_url, use_auth_token=hf_token))) == 0
+
+
 @pytest.mark.parametrize(
     "input_path, start_path, expected_path",
     [