We investigate theoretically the nonlinear state of ideal straight rolls in
the Rayleigh-B\'enard system of a fluid layer heated from below with a porous
medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation,
binary mixtures with positive separation ratio are studied and compared to
one-component fluids. Our results for the structural properties of roll
convection resemble qualitatively the situation in the Rayleigh--B\'enard
system without porous medium except for the fact that the streamlines of binary
mixtures are deformed in the so-called Soret regime. The deformation of the
streamlines is explained by means of the Darcy equation which is used to
describe the transport of momentum. In addition to the properties of the rolls,
their stability against arbitrary infinitesimal perturbations is investigated.
We compute stability balloons for the pure fluid case as well as for a wide
parameter range of Lewis numbers and separation ratios which are typical for
binary gas and fluid mixtures. The stability regions of rolls are found to be
restricted by a crossroll, a zigzag and a new type of oscillatory instability
mechanism, which can be related to the crossroll mechanism