Effect of anisotropy on the onset of natural convection heat transfer in a fluid saturated porous horizontal cavity subjected to nonuniform thermal gradients is investigated analytically. The porous layer is heated from the bottom by a constant heat flux while the other surfaces are being insulated. The horizontal boundaries are either rigid/rigid or stress-free/stress-free. The hydrodynamic anisotropy of the porous matrix is considered. The principal directions of the permeability are oriented in a direction that is oblique to the gravity. Based on a parallel flow assumption, closed-form solution for the flow and heat transfer variables, valid for the onset of convection corresponding to vanishingly small wave number, is obtained in terms of the Darcy-Rayleigh number Ra, the Darcy number Da, and the anisotropic parameters K* and theta. The critical Rayleigh number for the onset of convection arising from sudden heating and cooling at the boundaries is also predicted. The limiting cases Da --> infinity (for a viscous pure fluid) and Da-->0 (for anisotropic porous media) completed all results. It is demonstrated that effects of anisotropic parameters are strongly significant.