diff --git a/src/fillalgebra.jl b/src/fillalgebra.jl
index 928c04a7..c17e46cd 100644
--- a/src/fillalgebra.jl
+++ b/src/fillalgebra.jl
@@ -551,3 +551,6 @@ end
 function LinearAlgebra.istril(A::AbstractFillMatrix, k::Integer = 0)
     iszero(A) || k >= size(A,2)-1
 end
+
+triu(A::AbstractZerosMatrix, k::Integer=0) = A
+tril(A::AbstractZerosMatrix, k::Integer=0) = A
diff --git a/src/oneelement.jl b/src/oneelement.jl
index 28bc2c4b..17c8309c 100644
--- a/src/oneelement.jl
+++ b/src/oneelement.jl
@@ -296,7 +296,20 @@ end
 adjoint(A::OneElementMatrix) = OneElement(adjoint(A.val), reverse(A.ind), reverse(A.axes))
 transpose(A::OneElementMatrix) = OneElement(transpose(A.val), reverse(A.ind), reverse(A.axes))
 
+# tril/triu
+
+function tril(A::OneElementMatrix, k::Integer=0)
+    nzband = A.ind[2] - A.ind[1]
+    OneElement(nzband > k ? zero(A.val) : A.val, A.ind, axes(A))
+end
+
+function triu(A::OneElementMatrix, k::Integer=0)
+    nzband = A.ind[2] - A.ind[1]
+    OneElement(nzband < k ? zero(A.val) : A.val, A.ind, axes(A))
+end
+
 # broadcast
+
 function broadcasted(::DefaultArrayStyle{N}, ::typeof(conj), r::OneElement{<:Any,N}) where {N}
     OneElement(conj(r.val), r.ind, axes(r))
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index e7a5eda6..ddc248e3 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -2447,6 +2447,17 @@ end
         @test A / (2 + 3.0im) === OneElement(val / (2 + 3.0im), (2,2), (3,4)) == B / (2 + 3.0im)
     end
 
+
+    @testset "tril/triu" begin
+        for A in (OneElement(3, (4,2), (4,5)), OneElement(3, (2,3), (4,5)), OneElement(3, (3,3), (4,5)))
+            B = Array(A)
+            for k in -5:5
+                @test tril(A, k) == tril(B, k)
+                @test triu(A, k) == triu(B, k)
+            end
+        end
+    end
+
     @testset "broadcasting" begin
         for v in (OneElement(2, 3, 4), OneElement(2im, (1,2), (3,4)))
             w = Array(v)
@@ -2634,3 +2645,11 @@ end
         end
     end
 end
+
+@testset "triu/tril for Zeros" begin
+    Z = Zeros(3, 4)
+    @test triu(Z) === Z
+    @test tril(Z) === Z
+    @test triu(Z, 2) === Z
+    @test tril(Z, 2) === Z
+end