diff --git a/Project.toml b/Project.toml
index 673df031..eb8e049f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,20 +3,23 @@ uuid = "90137ffa-7385-5640-81b9-e52037218182"
 version = "1.5.2"
 
 [deps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
-julia = "1.6"
 StaticArraysCore = "1"
+julia = "1.6"
 
 [extras]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 
 [targets]
-test = ["InteractiveUtils", "Test", "BenchmarkTools", "OffsetArrays"]
+test = ["InteractiveUtils", "Test", "BenchmarkTools", "OffsetArrays", "Zygote", "ForwardDiff"]
diff --git a/src/StaticArrays.jl b/src/StaticArrays.jl
index e2e3fd83..7b353f84 100644
--- a/src/StaticArrays.jl
+++ b/src/StaticArrays.jl
@@ -12,6 +12,7 @@ import Statistics: mean
 
 using Random
 import Random: rand, randn, randexp, rand!, randn!, randexp!
+using ChainRulesCore
 using Core.Compiler: return_type
 import Base: sqrt, exp, log, float, real
 using LinearAlgebra
@@ -129,6 +130,7 @@ include("io.jl")
 include("pinv.jl")
 
 include("precompile.jl")
+include("chainrule.jl")
 _precompile_()
 
 end # module
diff --git a/src/chainrule.jl b/src/chainrule.jl
new file mode 100644
index 00000000..f177081c
--- /dev/null
+++ b/src/chainrule.jl
@@ -0,0 +1,23 @@
+### Projecting a tuple to SMatrix leads to ChainRulesCore._projection_mismatch by default, so overloaded here
+function (project::ChainRulesCore.ProjectTo{<:Tangent{<:Tuple}})(dx::SArray)
+    dy = reshape(dx, axes(project.elements))  # allows for dx::OffsetArray
+    dz = ntuple(i -> project.elements[i](dy[i]), length(project.elements))
+    return ChainRulesCore.project_type(project)(dz...)
+end
+
+### Project SArray to SArray
+function ChainRulesCore.ProjectTo(x::SArray{S,T}) where {S, T}
+    return ChainRulesCore.ProjectTo{SArray}(; element=ChainRulesCore._eltype_projectto(T), axes=S)
+end
+
+function (project::ChainRulesCore.ProjectTo{SArray})(dx::AbstractArray{S,M}) where {S,M}
+    return SArray{project.axes}(dx)
+end
+
+### Adjoint for SArray constructor
+
+function ChainRulesCore.rrule(::Type{T}, x::Tuple) where {T<:SArray}
+    project_x = ProjectTo(x)
+    Array_pullback(ȳ) = (NoTangent(), project_x(ȳ))
+    return T(x), Array_pullback
+end
\ No newline at end of file
diff --git a/test/abstractarray.jl b/test/abstractarray.jl
index d8aff256..8fc6c917 100644
--- a/test/abstractarray.jl
+++ b/test/abstractarray.jl
@@ -1,4 +1,4 @@
-using StaticArrays, Test, LinearAlgebra
+using StaticArrays, Test, LinearAlgebra, Zygote, ForwardDiff
 
 @testset "AbstractArray interface" begin
     @testset "size and length" begin
@@ -243,6 +243,43 @@ using StaticArrays, Test, LinearAlgebra
             @test rs == Base.reduced_indices(axes(a), i)
         end
     end
+
+    @testset "AutoDiff" begin
+        u0 = @SVector rand(2)
+        p = @SVector rand(4)
+
+        function lotka(u, p, svec=true)
+            du1 = p[1]*u[1] - p[2]*u[1]*u[2]
+            du2 = -p[3]*u[2] + p[4]*u[1]*u[2]
+            if svec
+                @SVector [du1, du2]
+            else
+                @SMatrix [du1 du2 du1; du2 du1 du1]
+            end
+        end
+
+        #SVector constructor adjoint
+        function loss(p)
+            u = lotka(u0, p)
+            sum(1 .- u)
+        end
+        
+        grad = Zygote.gradient(loss, p)
+        @test typeof(grad[1]) <: SArray
+        grad2 = ForwardDiff.gradient(loss, p)
+        @test grad[1] ≈ grad2 rtol=1e-12
+        
+        #SMatrix constructor adjoint
+        function loss_mat(p)
+            u = lotka(u0, p, false)
+            sum(1 .- u)
+        end
+
+        grad = Zygote.gradient(loss_mat, p)
+        @test typeof(grad[1]) <: SArray
+        grad2 = ForwardDiff.gradient(loss_mat, p)
+        @test grad[1] ≈ grad2 rtol=1e-12
+    end
 end
 
 @testset "permutedims" begin