diff --git a/test/fp_groups.jl b/test/fp_groups.jl
new file mode 100644
index 0000000..3e7d37e
--- /dev/null
+++ b/test/fp_groups.jl
@@ -0,0 +1,44 @@
+@testset "FPGroups" begin
+    A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5])
+
+    F = New.FreeGroup([:a, :b, :c], A)
+
+    a,b,c = gens(F)
+    @test c*b*a isa New.FPGroupElement
+
+    # quotient of F:
+    G = New.FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b])
+
+    @test G isa New.FPGroup
+    @test rand(G) isa New.FPGroupElement
+
+    f = a*c*b
+    @test New.word(f) isa Word{UInt8}
+
+    aG,bG,cG = gens(G)
+
+    @test aG isa New.FPGroupElement
+    @test_throws AssertionError aG == a
+    @test New.word(aG) == New.word(a)
+
+    g = aG*cG*bG
+
+    @test_throws AssertionError f == g
+    @test New.word(f) == New.word(g)
+    @test New.word(g) == [1, 5, 3]
+    New.normalform!(g)
+    @test New.word(g) == [1, 3, 5]
+
+    # quotient of G
+    H = New.FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200)
+
+    h = H(New.word(g))
+
+    @test h isa New.FPGroupElement
+    @test_throws AssertionError h == g
+    @test_throws AssertionError h*g
+
+    New.normalform!(h)
+    @test h == H([5])
+
+end
diff --git a/test/free_groups.jl b/test/free_groups.jl
new file mode 100644
index 0000000..007292e
--- /dev/null
+++ b/test/free_groups.jl
@@ -0,0 +1,65 @@
+@testset "New.FreeGroup" begin
+
+    A3 = Alphabet([:a, :b, :c, :A, :B, :C], [4,5,6,1,2,3])
+    F3 = New.FreeGroup([:a, :b, :c], A3)
+    @test F3 isa New.FreeGroup
+
+    @test gens(F3) isa Vector
+
+    @test eltype(F3) <: New.FPGroupElement{<:New.FreeGroup}
+
+    w = F3([1,2,3,4])
+    W = inv(w)
+    @test deepcopy(w) !== w
+    @test deepcopy(w).word !== w.word
+
+    @test isone(w*W)
+
+    @test New.alphabet(w) == A3
+
+    @testset "generic iteration" begin
+        w, s = iterate(F3)
+        @test isone(w)
+        w, s = iterate(F3, s)
+        @test w == gens(F3, 1)
+
+        a,b,c = gens(F3)
+
+        function test_iteration(F, n=1000)
+            w, s = iterate(F)
+            for i in 1:n
+                w, s = iterate(F, s)
+            end
+            return w
+        end
+
+        k = test_iteration(F3, 10)
+        @test k == a*b^-1
+
+        @time k = test_iteration(F3, 1000)
+        @test k == (a^2)*c^2*a^-1
+    end
+
+    @testset "wl_ball" begin
+        function wl_ball(F; radius::Integer)
+            g, state = iterate(F)
+            while length(New.word(g)) <= radius
+                res = iterate(F, state)
+                isnothing(res) && break
+                g, state = res
+            end
+            elts = collect(first(state).elts)
+            elts = resize!(elts, length(elts)-1)
+            return elts
+        end
+
+        E4 = wl_ball(F3, radius=4)
+        @test length(E4) == 937
+        @test New.word(last(E4)) == Word([6])^4
+
+        @time E8 = wl_ball(F3, radius=8)
+        @test length(E8) == 585937
+        @test New.word(last(E8)) == Word([6])^8
+    end
+
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 8fd5944..212c369 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -23,4 +23,12 @@ using LinearAlgebra
    include("FreeGroup-tests.jl")
    include("AutGroup-tests.jl")
    include("FPGroup-tests.jl")
+
+   @testset "New FPGroups" begin
+      using Groups.New
+      using KnuthBendix
+
+      include("free_groups.jl")
+      include("fp_groups.jl")
+   end
 end