diff --git a/src/bijectors/composed.jl b/src/bijectors/composed.jl
index 43b319dd..0d1c85d7 100644
--- a/src/bijectors/composed.jl
+++ b/src/bijectors/composed.jl
@@ -94,6 +94,13 @@ end
 
 isclosedform(b::Composed) = all(isclosedform, b.ts)
 up1(b::Composed) = Composed(up1.(b.ts))
+function Base.:(==)(b1::Composed{<:Any, N}, b2::Composed{<:Any, N}) where {N}
+    ts1, ts2 = b1.ts, b2.ts
+    if !(ts1 isa Tuple && ts2 isa Tuple || ts1 isa Vector && ts2 isa Vector)
+        return false
+    end
+    return all(ts1 .== ts2)
+end
 
 """
     composel(ts::Bijector...)::Composed{<:Tuple}
diff --git a/src/bijectors/logit.jl b/src/bijectors/logit.jl
index f0f6386d..f342b837 100644
--- a/src/bijectors/logit.jl
+++ b/src/bijectors/logit.jl
@@ -12,6 +12,8 @@ function Logit(a, b)
     Logit{0, T}(a, b)
 end
 up1(b::Logit{N, T}) where {N, T} = Logit{N + 1, T}(b.a, b.b)
+# For equality of Logit with Float64 fields to one with Duals
+Base.:(==)(b1::Logit, b2::Logit) = b1.a == b2.a && b1.b == b2.b
 
 (b::Logit{0})(x::Real) = _logit(x, b.a, b.b)
 (b::Logit{0})(x) = _logit.(x, b.a, b.b)
@@ -36,4 +38,4 @@ logabsdetjac(b::Logit{2}, x::AbstractMatrix) = sum(logit_logabsdetjac.(x, b.a, b
 logabsdetjac(b::Logit{2}, x::AbstractArray{<:AbstractMatrix}) = map(x) do x
     logabsdetjac(b, x)
 end
-logit_logabsdetjac(x, a, b) = -log((x - a) * (b - x) / (b - a))
\ No newline at end of file
+logit_logabsdetjac(x, a, b) = -log((x - a) * (b - x) / (b - a))
diff --git a/src/bijectors/normalise.jl b/src/bijectors/normalise.jl
index 4bb8ded9..300c46e2 100644
--- a/src/bijectors/normalise.jl
+++ b/src/bijectors/normalise.jl
@@ -14,6 +14,14 @@ mutable struct InvertibleBatchNorm{T1,T2,T3} <: Bijector{1}
     eps     ::  T3
     mtm     ::  T3  # momentum
 end
+function Base.:(==)(b1::InvertibleBatchNorm, b2::InvertibleBatchNorm)
+    return  b1.b == b2.b && 
+            b1.logs == b2.logs &&
+            b1.m == b2.m &&
+            b1.v == b2.v &&
+            b1.eps == b2.eps &&
+            b1.mtm == b2.mtm
+end
 
 function InvertibleBatchNorm(
     chs::Int;
diff --git a/src/bijectors/permute.jl b/src/bijectors/permute.jl
index 9fc86bfc..d4fdef7b 100644
--- a/src/bijectors/permute.jl
+++ b/src/bijectors/permute.jl
@@ -85,6 +85,8 @@ struct Permute{A} <: Bijector{1}
     A::A
 end
 
+Base.:(==)(b1::Permute, b2::Permute) = b1.A == b2.A
+
 function Permute(indices::AbstractVector{Int})
     # construct a sparse-matrix for use in the multiplication
     n = length(indices)
diff --git a/src/bijectors/planar_layer.jl b/src/bijectors/planar_layer.jl
index 03063fbd..a38a6be0 100644
--- a/src/bijectors/planar_layer.jl
+++ b/src/bijectors/planar_layer.jl
@@ -20,6 +20,9 @@ mutable struct PlanarLayer{T1<:AbstractVector{<:Real}, T2<:Real} <: Bijector{1}
     u::T1
     b::T2
 end
+function Base.:(==)(b1::PlanarLayer, b2::PlanarLayer)
+    return b1.w == b2.w && b1.u == b2.u && b1.b == b2.b
+end
 
 function get_u_hat(u, w)
     # To preserve invertibility
diff --git a/src/bijectors/radial_layer.jl b/src/bijectors/radial_layer.jl
index 5bade504..2f4367b1 100644
--- a/src/bijectors/radial_layer.jl
+++ b/src/bijectors/radial_layer.jl
@@ -18,6 +18,9 @@ mutable struct RadialLayer{T1 <: Real, T2 <: AbstractVector{<:Real}} <: Bijector
     β::T1
     z_0::T2
 end
+function Base.:(==)(b1::RadialLayer, b2::RadialLayer)
+    return b1.α_ == b2.α_ && b1.β == b2.β && b1.z_0 == b2.z_0
+end
 
 function RadialLayer(dims::Int, container=Array)
     α_ = randn()
diff --git a/src/bijectors/scale.jl b/src/bijectors/scale.jl
index 55305796..5d728a05 100644
--- a/src/bijectors/scale.jl
+++ b/src/bijectors/scale.jl
@@ -2,6 +2,8 @@ struct Scale{T, N} <: Bijector{N}
     a::T
 end
 
+Base.:(==)(b1::Scale{<:Any, N}, b2::Scale{<:Any, N}) where {N} = b1.a == b2.a
+
 function Scale(a::Union{Real,AbstractArray}; dim::Val{D} = Val(ndims(a))) where D
     return Scale{typeof(a), D}(a)
 end
diff --git a/src/bijectors/shift.jl b/src/bijectors/shift.jl
index 3017ff99..ab975bb5 100644
--- a/src/bijectors/shift.jl
+++ b/src/bijectors/shift.jl
@@ -5,6 +5,8 @@ struct Shift{T, N} <: Bijector{N}
     a::T
 end
 
+Base.:(==)(b1::Shift{<:Any, N}, b2::Shift{<:Any, N}) where {N} = b1.a == b2.a
+
 function Shift(a::Union{Real,AbstractArray}; dim::Val{D} = Val(ndims(a))) where D
     return Shift{typeof(a), D}(a)
 end
diff --git a/src/bijectors/stacked.jl b/src/bijectors/stacked.jl
index 37397d2d..d5b3faf6 100644
--- a/src/bijectors/stacked.jl
+++ b/src/bijectors/stacked.jl
@@ -44,6 +44,14 @@ end
 Stacked(bs, ranges::AbstractArray) = Stacked(bs, tuple(ranges...))
 Stacked(bs) = Stacked(bs, tuple([i:i for i = 1:length(bs)]...))
 
+function Base.:(==)(b1::Stacked, b2::Stacked)
+    bs1, bs2 = b1.bs, b2.bs
+    if !(bs1 isa Tuple && bs2 isa Tuple || bs1 isa Vector && bs2 isa Vector)
+        return false
+    end
+    return all(bs1 .== bs2) && all(b1.ranges .== b2.ranges)
+end
+
 isclosedform(b::Stacked) = all(isclosedform, b.bs)
 
 stack(bs::Bijector{0}...) = Stacked(bs)
diff --git a/src/bijectors/truncated.jl b/src/bijectors/truncated.jl
index 2cb95e6b..e403f988 100644
--- a/src/bijectors/truncated.jl
+++ b/src/bijectors/truncated.jl
@@ -11,6 +11,10 @@ function TruncatedBijector{N}(lb::T1, ub::T2) where {N, T1, T2}
 end
 up1(b::TruncatedBijector{N}) where {N} = TruncatedBijector{N + 1}(b.lb, b.ub)
 
+function Base.:(==)(b1::TruncatedBijector, b2::TruncatedBijector)
+    return b1.lb == b2.lb && b1.ub == b2.ub
+end
+
 function (b::TruncatedBijector{0})(x::Real)
     a, b = b.lb, b.ub
     truncated_link(_clamp(x, a, b), a, b)
diff --git a/src/interface.jl b/src/interface.jl
index a5ec2754..656b3912 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -70,6 +70,7 @@ up1(b::Inverse) = Inverse(up1(b.orig))
 
 inv(b::Bijector) = Inverse(b)
 inv(ib::Inverse{<:Bijector}) = ib.orig
+Base.:(==)(b1::Inverse{<:Bijector}, b2::Inverse{<:Bijector}) = b1.orig == b2.orig
 
 """
     logabsdetjac(b::Bijector, x)
diff --git a/test/interface.jl b/test/interface.jl
index 7000f1da..31b0eadc 100644
--- a/test/interface.jl
+++ b/test/interface.jl
@@ -5,7 +5,7 @@ using ForwardDiff
 using Tracker
 
 using Bijectors
-using Bijectors: Log, Exp, Shift, Scale, Logit, SimplexBijector, ADBijector
+using Bijectors: Log, Exp, Shift, Scale, Logit, SimplexBijector, PDBijector, Permute, PlanarLayer, RadialLayer, Stacked, TruncatedBijector, ADBijector
 
 Random.seed!(123)
 
@@ -599,7 +599,7 @@ end
     @test res.rv == [exp(x[1]), log(x[2]), x[3] + 5.0]
     @test logabsdetjac(sb, x) == sum([sum(logabsdetjac(sb.bs[i], x[sb.ranges[i]])) for i = 1:3])
     @test res.logabsdetjac == logabsdetjac(sb, x)
-    
+
 
     # TODO: change when we have dimensionality in the type
     sb = @inferred Stacked((Bijectors.Exp(), Bijectors.SimplexBijector()), [1:1, 2:3])
@@ -735,4 +735,59 @@ end
     @test Δ_forwarddiff ≈ Δ_tracker
 end
 
+@testset "Equality" begin
+    bs = [
+        Identity{0}(),
+        Identity{1}(),
+        Identity{2}(),
+        Exp{0}(),
+        Exp{1}(),
+        Exp{2}(),
+        Log{0}(),
+        Log{1}(),
+        Log{2}(),
+        Scale(2.0),
+        Scale(3.0),
+        Scale(rand(2,2)),
+        Scale(rand(2,2)),
+        Shift(2.0),
+        Shift(3.0),
+        Shift(rand(2)),
+        Shift(rand(2)),
+        Logit(1.0, 2.0),
+        Logit(1.0, 3.0),
+        Logit(2.0, 3.0),
+        Logit(0.0, 2.0),
+        InvertibleBatchNorm(2),
+        InvertibleBatchNorm(3),
+        PDBijector(),
+        Permute([1.0, 2.0, 3.0]),
+        Permute([2.0, 3.0, 4.0]),
+        PlanarLayer(2),
+        PlanarLayer(3),
+        RadialLayer(2),
+        RadialLayer(3),
+        SimplexBijector(),
+        Stacked((Exp{0}(), Log{0}())),
+        Stacked((Log{0}(), Exp{0}())),
+        Stacked([Exp{0}(), Log{0}()]),
+        Stacked([Log{0}(), Exp{0}()]),
+        Composed((Exp{0}(), Log{0}())),
+        Composed((Log{0}(), Exp{0}())),
+        Composed([Exp{0}(), Log{0}()]),
+        Composed([Log{0}(), Exp{0}()]),
+        TruncatedBijector(1.0, 2.0),
+        TruncatedBijector(1.0, 3.0),
+        TruncatedBijector(0.0, 2.0),
+    ]
+    for i in 1:length(bs), j in 1:length(bs)
+        if i == j
+            @test bs[i] == deepcopy(bs[j])
+            @test inv(bs[i]) == inv(deepcopy(bs[j]))
+        else
+            @test bs[i] != bs[j]
+        end
+    end
+end
+
 include("norm_flows.jl")
\ No newline at end of file