diff --git a/Project.toml b/Project.toml
index 3e04e2f..83f1256 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "DiffRules"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.11.0"
+version = "1.11.1"
 
 [deps]
 IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
diff --git a/src/rules.jl b/src/rules.jl
index 45104aa..6e4a1fa 100644
--- a/src/rules.jl
+++ b/src/rules.jl
@@ -248,11 +248,14 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
 @define_diffrule LogExpFunctions.logmxp1(x) = :((1 - $x) / $x)
 
 # binary
-@define_diffrule LogExpFunctions.xlogy(x, y) = :(log($y)), :($x / $y)
+@define_diffrule LogExpFunctions.xlogy(x, y) = 
+    :(log($y)),
+    :(z = $x / $y; iszero($x) && !isnan($y) ? zero(z) : z)
 @define_diffrule LogExpFunctions.logaddexp(x, y) =
     :(exp($x - LogExpFunctions.logaddexp($x, $y))), :(exp($y - LogExpFunctions.logaddexp($x, $y)))
 @define_diffrule LogExpFunctions.logsubexp(x, y) =
     :(z = LogExpFunctions.logsubexp($x, $y); $x > $y ? exp($x - z) : -exp($x - z)),
     :(z = LogExpFunctions.logsubexp($x, $y); $x > $y ? -exp($y - z) : exp($y - z))
-
-@define_diffrule LogExpFunctions.xlog1py(x, y) = :(log1p($y)), :($x / (1 + $y))
+@define_diffrule LogExpFunctions.xlog1py(x, y) = 
+    :(log1p($y)),
+    :(z = $x / (1 + $y); iszero($x) && !isnan($y) ? zero(z) : z)
diff --git a/test/runtests.jl b/test/runtests.jl
index fa75616..3312f7f 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -141,6 +141,40 @@ for xtype in [:Float64, :BigFloat]
     end
 end
 
+# Test `iszero(x)` branch of `xlogy`
+derivs = DiffRules.diffrule(:LogExpFunctions, :xlogy, :x, :y)
+for xytype in [:Float32, :Float64, :BigFloat]
+    @eval begin
+        let
+            x = zero($xytype)
+            y = rand($xytype)
+            dx, dy = $(derivs[1]), $(derivs[2])
+            @test iszero(dy)
+
+            y = one($xytype)
+            dx, dy = $(derivs[1]), $(derivs[2])
+            @test iszero(dy)
+        end
+    end
+end
+
+# Test `iszero(x)` branch of `xlog1py`
+derivs = DiffRules.diffrule(:LogExpFunctions, :xlog1py, :x, :y)
+for xytype in [:Float32, :Float64, :BigFloat]
+    @eval begin
+        let
+            x = zero($xytype)
+            y = rand($xytype)
+            dx, dy = $(derivs[1]), $(derivs[2])
+            @test iszero(dy)
+
+            y = -one($xytype)
+            dx, dy = $(derivs[1]), $(derivs[2])
+            @test iszero(dy)
+        end
+    end
+end
+
 end
 
     @testset "diffrules" begin