  We study the anisotropic Forchheimer-typed flows for compressible fluids in
porous media. The first half of the paper is devoted to understanding the
nonlinear structure of the anisotropic momentum equations. Unlike the isotropic
flows, the important monotonicity properties are not automatically satisfied in
this case. Therefore, various sufficient conditions for them are derived and
applied to the experimental data. In the second half of the paper, we prove the
existence and uniqueness of the steady state flows subject to a nonhomogeneous
Dirichlet boundary condition. It is also established that these steady states,
in appropriate functional spaces, have local H\"older continuous dependence on
the forcing function and the boundary data.
