diff --git a/Manifest.toml b/Manifest.toml
index 84230b42f5..a6aa43b692 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -105,10 +105,10 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
 [[NNlib]]
-deps = ["Libdl", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
-git-tree-sha1 = "a8180fd1445e31c0b1add98dae8da694ac2c23fd"
+deps = ["Compat", "Libdl", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
+git-tree-sha1 = "1ae42464fea5258fd2ff49f1c4a40fc41cba3860"
 uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-version = "0.7.6"
+version = "0.7.7"
 
 [[OrderedCollections]]
 git-tree-sha1 = "cf59cfed2e2c12e8a2ff0a4f1e9b2cd8650da6db"
diff --git a/Project.toml b/Project.toml
index 132993f12a..cf7ae821cd 100644
--- a/Project.toml
+++ b/Project.toml
@@ -37,7 +37,7 @@ GPUArrays = "6.1.0"
 GPUCompiler = "0.8.1"
 LLVM = "3"
 MacroTools = "0.5"
-NNlib = "0.6.5, 0.7"
+NNlib = "0.7.7"
 Reexport = "0.2"
 Requires = "0.5, 1.0"
 TimerOutputs = "0.5"
diff --git a/lib/cublas/wrappers.jl b/lib/cublas/wrappers.jl
index b2682cae8a..68e8a2fd88 100644
--- a/lib/cublas/wrappers.jl
+++ b/lib/cublas/wrappers.jl
@@ -923,15 +923,16 @@ for (fname, elty) in
         function gemm_strided_batched!(transA::Char,
                                transB::Char,
                                alpha::Number,
-                               A::DenseCuArray{$elty, 3},
-                               B::DenseCuArray{$elty, 3},
+                               A::AbstractArray{$elty, 3}, # allow PermutedDimsArray
+                               B::AbstractArray{$elty, 3},
                                beta::Number,
-                               C::DenseCuArray{$elty, 3})
+                               C::AbstractArray{$elty, 3})
            m = size(A, transA == 'N' ? 1 : 2)
            k = size(A, transA == 'N' ? 2 : 1)
            n = size(B, transB == 'N' ? 2 : 1)
 
-           @assert size(A, 3) == size(B, 3) == size(C, 3) "Batch size mismatch"
+           @assert size(A, 3) == size(C, 3) || size(A, 3) == 1 "batch size mismatch: A != C"
+           @assert size(B, 3) == size(C, 3) || size(B, 3) == 1 "batch size mismatch: B != C"
 
            if m != size(C,1) || n != size(C,2) || k != size(B, transB == 'N' ? 1 : 2)
                throw(DimensionMismatch(""))
@@ -940,10 +941,10 @@ for (fname, elty) in
            ldb = max(1,stride(B,2))
            ldc = max(1,stride(C,2))
 
-           strideA = stride(A, 3)
-           strideB = stride(B, 3)
+           strideA = size(A, 3) == 1 ? 0 : stride(A, 3)
+           strideB = size(B, 3) == 1 ? 0 : stride(B, 3)
            strideC = stride(C, 3)
-           batchCount = size(A, 3)
+           batchCount = size(C, 3)
            $fname(handle(), transA, transB, m, n, k, alpha, A, lda, strideA, B,
                   ldb, strideB, beta, C, ldc, strideC, batchCount)
            C
@@ -951,15 +952,15 @@ for (fname, elty) in
         function gemm_strided_batched(transA::Char,
                       transB::Char,
                       alpha::Number,
-                      A::DenseCuArray{$elty, 3},
-                      B::DenseCuArray{$elty, 3})
-            C = similar(B, (size(A, transA == 'N' ? 1 : 2), size(B, transB == 'N' ? 2 : 1), size(A, 3)))
+                      A::AbstractArray{$elty, 3},
+                      B::AbstractArray{$elty, 3})
+            C = similar(B, (size(A, transA == 'N' ? 1 : 2), size(B, transB == 'N' ? 2 : 1), max(size(A, 3), size(B, 3))))
             gemm_strided_batched!(transA, transB, alpha, A, B, zero($elty), C )
         end
         function gemm_strided_batched(transA::Char,
                       transB::Char,
-                      A::DenseCuArray{$elty, 3},
-                      B::DenseCuArray{$elty, 3})
+                      A::AbstractArray{$elty, 3},
+                      B::AbstractArray{$elty, 3})
             gemm_strided_batched(transA, transB, one($elty), A, B)
         end
     end
diff --git a/src/array.jl b/src/array.jl
index d63daf3c3f..f790545774 100644
--- a/src/array.jl
+++ b/src/array.jl
@@ -429,6 +429,12 @@ function Base.unsafe_convert(::Type{CuPtr{T}}, V::SubArray{T,N,P,<:Tuple{Vararg{
 end
 
 
+## PermutedDimsArray
+
+Base.unsafe_convert(::Type{CuPtr{T}}, A::PermutedDimsArray) where {T} =
+    Base.unsafe_convert(CuPtr{T}, parent(A))
+
+
 ## reshape
 
 # optimize reshape to return a CuArray
diff --git a/src/nnlib.jl b/src/nnlib.jl
index 9ffdba88ee..1cf65bdd26 100644
--- a/src/nnlib.jl
+++ b/src/nnlib.jl
@@ -23,16 +23,9 @@ end
 
 
 # Batched matrix multiplication
+# 1st argument is produced by NNlib.storage_type(A)
+NNlib._batched_gemm!(::Type{<:CuArray}, transA::Char, transB::Char, α::Number, A, B, β::Number, C) =
+     CUBLAS.gemm_strided_batched!(transA, transB, α, A, B, β, C)
 
-const batched_gemm_args = [
-    (:(CuArray{T, 3}), 'N'),
-    (:(NNlib.BatchedTranspose{T, <:CuArray{T, 3}}), 'T'),
-    (:(NNlib.BatchedAdjoint{T, <:CuArray{T, 3}}), 'C')
-]
-
-for (TA, transA) in batched_gemm_args, (TB, transB) in batched_gemm_args
-    @eval function NNlib.batched_mul!(C::CuArray{T, 3}, A::$TA, B::$TB) where {T<:CUBLAS.CublasFloat}
-        CUBLAS.gemm_strided_batched!($transA, $transB, one(T), NNlib._unbatch(A), NNlib._unbatch(B), zero(T), C)
-        C
-    end
-end
+Base.unsafe_convert(::Type{CuPtr{T}}, A::NNlib.BatchedAdjOrTrans{T}) where {T} =
+    Base.unsafe_convert(CuPtr{T}, parent(A))
diff --git a/test/nnlib.jl b/test/nnlib.jl
index 930b0a1b7d..8f57e27f90 100644
--- a/test/nnlib.jl
+++ b/test/nnlib.jl
@@ -1,7 +1,7 @@
 using NNlib
 
 @testset "batched_mul" begin
-    using NNlib: batched_mul, batched_adjoint, batched_transpose
+    using NNlib: batched_mul, batched_mul!, batched_vec, batched_adjoint, batched_transpose
 
     A = randn(Float32, 3,3,2);
     B = randn(Float32, 3,3,2);
@@ -14,6 +14,47 @@ using NNlib
 
     Ca = batched_mul(A, batched_adjoint(B))
     @test CuArray(Ca) ≈ batched_mul(CuArray(A), batched_adjoint(CuArray(B)))
+
+    # 5-arg batched_mul!
+    C .= pi
+    batched_mul!(C, A, B, 2f0, 3f0)
+    cuCpi = CuArray(similar(C)) .= pi
+    @test CuArray(C) ≈ batched_mul!(cuCpi, CuArray(A), CuArray(B), 2f0, 3f0)
+
+    # PermutedDimsArray
+    @test CuArray(Ct) ≈ batched_mul(PermutedDimsArray(CuArray(A), (2,1,3)), CuArray(B))
+
+    D = permutedims(B, (1,3,2))
+    Cp = batched_mul(batched_adjoint(A), B)
+    @test CuArray(Cp) ≈ batched_mul(batched_adjoint(CuArray(A)), PermutedDimsArray(CuArray(D), (1,3,2)))
+
+    # Methods which reshape
+    M = randn(Float32, 3,3)
+
+    Cm = batched_mul(A, M)
+    @test CuArray(Cm) ≈ batched_mul(CuArray(A), CuArray(M))
+
+    Cv = batched_vec(permutedims(A,(3,1,2)), M)
+    @test CuArray(Cv) ≈ batched_vec(PermutedDimsArray(CuArray(A),(3,1,2)), CuArray(M))
+end
+
+@testset "NNlib storage_type etc." begin
+    using LinearAlgebra
+    using NNlib: is_strided, are_strided, storage_type
+
+    M = cu(ones(10,10))
+
+    @test is_strided(M)
+    @test is_strided(view(M, 1:2:5,:))
+    @test is_strided(PermutedDimsArray(M, (2,1)))
+
+    @test !is_strided(reshape(view(M, 1:2:10,:), 10,:))
+    @test !is_strided((M .+ im)')
+    @test !is_strided(Diagonal(cu(ones(3))))
+
+    @test storage_type(M) == CuArray{Float32,2}
+    @test storage_type(reshape(view(M, 1:2:10,:), 10,:)) == CuArray{Float32,2}
+
 end
 
 @testset "Broadcast Fix" begin