A linear stability analysis of the single-phase conservation equation in multidimensional porous media is performed, for both weakly compressible and compressible fluids. Non-Newtonian and non-Darcy effects are accounted for using a non-linear Darcy-like form for the superficial velocity, where the mobility tensor is velocity-dependent and proportional to the permeability. It is found that under this hypothesis, flows at an angle with respect to the principal axes of the permeability tensor can be unstable, unless the mobility is a function of the velocity magnitude in terms of the inverse permeability norm. As shown by previous authors, for steady-state incompressible flows this is also the condition ensuring that the governing equation derives from the minimization of a dissipation potential.