The linear stability analysis is applied to a horizontal porous layer saturated with water in the neighborhood of 4degreesC. The porous layer considered is two-dimensional and anisotropic in permeability with principal axes arbitrarily oriented. The onset of convection depends on parameters such as the aspect ratio A, the permeability ratio K-*, the orientation angle, theta of the principal axes and the inversion parameter, gamma. The relevant linearized equations are solved with the aid of Galerkin and finite element methods. Results for the case of an infinite layer indicate that the presence of a stable layer near the upper boundary for gamma < 2 changes drastically the critical Rayleigh number and that an asymptotic situation is reached when gamma less than or equal to 1. For that asymptotic situation, and with theta = 0degrees or 90degrees, the incipient flow field consists of primary convective cells near the lower boundary with superposed layers of secondary cells. For 0degrees < theta < 90degrees, primary and secondary cells coalesce to form obliquely elongated cells.