diff --git a/test/basekernels/fbm.jl b/test/basekernels/fbm.jl
index 3fe58dd0a..4d2cad74b 100644
--- a/test/basekernels/fbm.jl
+++ b/test/basekernels/fbm.jl
@@ -13,7 +13,19 @@
 
     test_interface(k)
     @test repr(k) == "Fractional Brownian Motion Kernel (h = $(h))"
-    test_ADs(FBMKernel; ADs=[:ReverseDiff, :Zygote])
-    @test_broken "Tests failing for kernelmatrix(k, x) for ForwardDiff"
+    test_ADs(FBMKernel; ADs=[:ReverseDiff])
+
+    # Tests failing for ForwardDiff and Zygote@0.6 (obtained with Julia > 1.3).
+    # Related to: https://github.com/FluxML/Zygote.jl/issues/1036
+    @test_broken !isinf(ForwardDiff.gradient(x -> x[1]^x[2], [0.0, 0.9])[1])
+    if VERSION >= v"1.4.0"
+        f(x, y) = x^y
+        @test_broken !isinf(
+            Zygote.gradient((x, y) -> sum(f.(x, y)), zeros(1), fill(0.9, 1))[1][1]
+        )
+    else
+        test_ADs(FBMKernel; ADs=[:Zygote])
+    end
+
     test_params(k, ([h],))
 end