  We prove a continuous embedding that allows us to obtain a boundary trace
imbedding result for anisotropic Musielak-Orlicz spaces, which we then apply to
obtain an existence result for Neumann problems with nonlinearities on the
boundary associated to some anisotropic nonlinear elliptic equations in
Musielak-Orlicz spaces constructed from Musielak-Orlicz functions on which and
on their conjugates we do not assume the $\Delta_2$-condition. The uniqueness
is also studied.
