diff --git a/Project.toml b/Project.toml
index d1cdc2c..55acbb2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -8,20 +8,24 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
 [weakdeps]
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 
 [extensions]
 ThickNumbersForwardDiffExt = "ForwardDiff"
+ThickNumbersMooncakeExt = "Mooncake"
 
 [compat]
 DifferentiationInterface = "0.6"
 ForwardDiff = "0.10, 1"
 LinearAlgebra = "1"
+Mooncake = "0.4"
 julia = "1.9"
 
 [extras]
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["DifferentiationInterface", "ForwardDiff", "Test"]
+test = ["DifferentiationInterface", "ForwardDiff", "Mooncake", "Test"]
diff --git a/ThickNumbersInterfaceTests/test/testpackages/IntervalArith/src/IntervalArith.jl b/ThickNumbersInterfaceTests/test/testpackages/IntervalArith/src/IntervalArith.jl
index d32cc9e..2139a33 100644
--- a/ThickNumbersInterfaceTests/test/testpackages/IntervalArith/src/IntervalArith.jl
+++ b/ThickNumbersInterfaceTests/test/testpackages/IntervalArith/src/IntervalArith.jl
@@ -15,6 +15,7 @@ end
 Interval(lo, hi) = Interval(promote(lo, hi)...)
 Interval{T}(iv::Interval) where T = Interval{T}(iv.lo, iv.hi)
 Interval{T}(x::Number) where T = Interval{T}(x, x)
+Interval{T}(nt::@NamedTuple{lo::T, hi::T}) where T = Interval{T}(nt.lo, nt.hi)   # needed by Mooncake
 
 ThickNumbers.loval(x::Interval) = x.lo
 ThickNumbers.hival(x::Interval) = x.hi
diff --git a/ext/ThickNumbersMooncakeExt.jl b/ext/ThickNumbersMooncakeExt.jl
new file mode 100644
index 0000000..1599e15
--- /dev/null
+++ b/ext/ThickNumbersMooncakeExt.jl
@@ -0,0 +1,12 @@
+module ThickNumbersMooncakeExt
+
+using ThickNumbers
+using Mooncake
+
+Mooncake.tangent_type(::Type{TN}) where TN<:ThickNumber = TN
+Mooncake.fdata_type(::Type{TN}) where TN<:ThickNumber = Mooncake.NoFData
+Mooncake.rdata_type(::Type{TN}) where TN<:ThickNumber = TN
+Mooncake.zero_rdata(x::ThickNumber) = zero(x)
+Mooncake.increment_internal!!(::Mooncake.IncCache, x::TN, y::TN) where TN<:ThickNumber = x + y
+
+end
diff --git a/test/extensions/di.jl b/test/extensions/di.jl
index f059037..04e158b 100644
--- a/test/extensions/di.jl
+++ b/test/extensions/di.jl
@@ -1,6 +1,8 @@
 using ThickNumbers
 using DifferentiationInterface
 using ForwardDiff
+# using Enzyme: EnzymeCore
+using Mooncake
 
 using Test
 
@@ -12,7 +14,7 @@ using IntervalArith
     @test isempty(detect_ambiguities(ThickNumbers))
     @test isempty(detect_ambiguities(IntervalArith))
 
-    for backend in (AutoForwardDiff(), )
+    for backend in (AutoForwardDiff(), #=AutoEnzyme(mode=EnzymeCore.Forward), AutoEnzyme(mode=EnzymeCore.Reverse),=# AutoMooncake(config=nothing))
         a, b = Interval(1, 2), Interval(0, 0.1)
         f1(t) = a + t*b
         f2(x) = a + abs2(x)/2