diff --git a/src/Sets/Universe/UniverseModule.jl b/src/Sets/Universe/UniverseModule.jl
index 04a5a0f26e..fce05bb7b4 100644
--- a/src/Sets/Universe/UniverseModule.jl
+++ b/src/Sets/Universe/UniverseModule.jl
@@ -15,6 +15,7 @@ using ReachabilityBase.Require: require
                         translate, translate!, cartesian_product, intersection
 @reexport import ..LazySets: constrained_dimensions, linear_map_inverse,
                              tosimplehrep
+import Base: copy
 @reexport using ..API
 
 export Universe
@@ -25,6 +26,7 @@ include("an_element.jl")
 include("complement.jl")
 include("constraints.jl")
 include("constraints_list.jl")
+include("copy.jl")
 include("diameter.jl")
 include("dim.jl")
 include("isbounded.jl")
diff --git a/src/Sets/Universe/copy.jl b/src/Sets/Universe/copy.jl
new file mode 100644
index 0000000000..12d0005c25
--- /dev/null
+++ b/src/Sets/Universe/copy.jl
@@ -0,0 +1,4 @@
+# since there is only a single instance (per dimensionality), we do not copy
+function copy(U::Universe)
+    return U
+end
diff --git a/src/Sets/ZeroSet/ZeroSetModule.jl b/src/Sets/ZeroSet/ZeroSetModule.jl
index 159442f7d1..7a3133d947 100644
--- a/src/Sets/ZeroSet/ZeroSetModule.jl
+++ b/src/Sets/ZeroSet/ZeroSetModule.jl
@@ -10,12 +10,14 @@ using ReachabilityBase.Require: require
 @reexport import ..API: dim, isoperationtype, rand, rectify, reflect, ∈,
                         linear_map, scale, scale!, ρ, translate, minkowski_sum
 @reexport import ..LazySets: element
+import Base: copy
 @reexport using ..API
 
 export ZeroSet
 
 include("ZeroSet.jl")
 
+include("copy.jl")
 include("dim.jl")
 include("isoperationtype.jl")
 include("rand.jl")
diff --git a/src/Sets/ZeroSet/copy.jl b/src/Sets/ZeroSet/copy.jl
new file mode 100644
index 0000000000..8570313cdc
--- /dev/null
+++ b/src/Sets/ZeroSet/copy.jl
@@ -0,0 +1,4 @@
+# since there is only a single instance (per dimensionality), we do not copy
+function copy(Z::ZeroSet)
+    return Z
+end
diff --git a/test/Sets/Universe.jl b/test/Sets/Universe.jl
index 835a1a6272..a3ce44cc8b 100644
--- a/test/Sets/Universe.jl
+++ b/test/Sets/Universe.jl
@@ -30,6 +30,10 @@ for N in [Float64, Rational{Int}, Float32]
     # dim
     @test dim(U) == 2
 
+    # copy
+    U2 = copy(U)
+    @test U2 isa Universe{N} && dim(U2) == 2
+
     # support function and support vector
     @test ρ(N[0, 1], U) == N(Inf)
     @test ρ(N[0, 0], U) == zero(N)
diff --git a/test/Sets/ZeroSet.jl b/test/Sets/ZeroSet.jl
index cf783a1cdb..9c04de7b0c 100644
--- a/test/Sets/ZeroSet.jl
+++ b/test/Sets/ZeroSet.jl
@@ -5,6 +5,10 @@ for N in [Float64, Rational{Int}, Float32]
     Z = ZeroSet{N}(2)
     B = BallInf(ones(N, 2), N(1))
 
+    # copy
+    Z2 = copy(Z)
+    @test Z2 isa ZeroSet{N} && dim(Z2) == 2
+
     # isoperationtype
     @test !isoperationtype(ZeroSet)