diff --git a/CMakeLists.txt b/CMakeLists.txt
index 42847f3e..75d29ff6 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -99,7 +99,7 @@ string(REGEX REPLACE "^ | $" "" LIBS "${LIBS}")
 
 # tests
 enable_testing()
-foreach(execid dense_layer input1d_layer)
+foreach(execid input1d_layer dense_layer dense_network)
   add_executable(test_${execid} test/test_${execid}.f90)
   target_link_libraries(test_${execid} neural ${LIBS})
   add_test(test_${execid} bin/test_${execid})
diff --git a/test/test_dense_network.f90 b/test/test_dense_network.f90
new file mode 100644
index 00000000..9df7e71b
--- /dev/null
+++ b/test/test_dense_network.f90
@@ -0,0 +1,69 @@
+program test_dense_network
+  use iso_fortran_env, only: stderr => error_unit
+  use nf, only: dense, input, network
+  implicit none
+  type(network) :: net
+  logical :: ok = .true.
+
+  ! Minimal 2-layer network
+  net = network([ &
+    input(1), &
+    dense(1) &
+  ])
+
+  if (.not. size(net % layers) == 2) then
+    write(stderr, '(a)') 'dense network should have 2 layers.. failed'
+    ok = .false.
+  end if
+
+  if (.not. all(net % output([0.]) == 0.5)) then
+    write(stderr, '(a)') &
+      'dense network should output exactly 0.5 for input 0.. failed'
+    ok = .false.
+  end if
+
+  training: block
+    real :: x(1), y(1)
+    real :: tolerance = 1e-3
+    integer :: n
+    integer, parameter :: num_iterations = 1000 
+
+    x = [0.123]
+    y = [0.765]
+
+    do n = 1, num_iterations
+      call net % forward(x)
+      call net % backward(y)
+      call net % update(1.)
+      if (all(abs(net % output(x) - y) < tolerance)) exit
+    end do
+
+    if (.not. n <= num_iterations) then
+      write(stderr, '(a)') &
+        'dense network should converge in simple training.. failed'
+      ok = .false.
+    end if
+
+  end block training
+
+  ! A bit larger multi-layer network
+  net = network([ &
+    input(784), &
+    dense(30), &
+    dense(20), &
+    dense(10) &
+  ])
+
+  if (.not. size(net % layers) == 4) then
+    write(stderr, '(a)') 'dense network should have 4 layers.. failed'
+    ok = .false.
+  end if
+
+  if (ok) then
+    print '(a)', 'test_dense_network: All tests passed.'
+  else
+    write(stderr, '(a)') 'test_dense_network: One or more tests failed.'
+    stop 1
+  end if
+
+end program test_dense_network