diff --git a/src/tangent_arithmetic.jl b/src/tangent_arithmetic.jl
index 18ae7b3ad..f79957311 100644
--- a/src/tangent_arithmetic.jl
+++ b/src/tangent_arithmetic.jl
@@ -146,6 +146,7 @@ Base.:+(a::Dict, d::Tangent{P}) where {P} = merge(+, a, backing(d))
 Base.:+(a::StructuralTangent{P}, b::P) where {P} = b + a
 
 Base.:-(tangent::StructuralTangent{P}) where {P} = map(-, tangent)
+Base.:-(a::StructuralTangent{P}, b::StructuralTangent{P}) where {P} = a + (-b)
 
 # We intentionally do not define, `Base.*(::Tangent, ::Tangent)` as that is not meaningful
 # In general one doesn't have to represent multiplications of 2 tangents
diff --git a/test/tangent_types/structural_tangent.jl b/test/tangent_types/structural_tangent.jl
index c177b05f4..d93487703 100644
--- a/test/tangent_types/structural_tangent.jl
+++ b/test/tangent_types/structural_tangent.jl
@@ -358,6 +358,24 @@ end
             @test -1.0 * t == -t
         end
 
+        @testset "subtraction" begin
+            a = Tangent{Foo}(; x=2.0, y=-2.0)
+            b = Tangent{Foo}(; x=1.0, y=2.0)
+            @test (a - b) == Tangent{Foo}(; x=1.0, y=-4.0)
+
+            a = Tangent{Foo}(; x=2.0, y=-2.0)
+            b = Tangent{Foo}(; x=1.0)
+            @test (a - b) == Tangent{Foo}(; x=1.0, y=-2.0)
+
+            a = Tangent{Tuple{Float64,Float64}}(2.0, 3.0)
+            b = Tangent{Tuple{Float64,Float64}}(1.0, 1.0)
+            @test (a - b) == Tangent{Tuple{Float64,Float64}}(1.0, 2.0)
+
+            a = MutableTangent{MFoo}(; x=1.5, y=1.5)
+            b = MutableTangent{MFoo}(; x=0.5, y=0.5)
+            @test (a - b) == MutableTangent{MFoo}(; x=1.0, y=1.0)
+        end
+
         @testset "scaling" begin
             @test (
                 2 * Tangent{Foo}(; y=1.5, x=2.5) ==