<p>This study examines the linear and weakly nonlinear stability of thermal convection in a fluid-saturated porous layer with couple stress, incorporating the Cattaneo heat-flux law under local thermal nonequilibrium conditions. The Cattaneo effect transforms the classical parabolic heat equation for the solid phase into a hyperbolic form, thereby enabling the propagation of temperature waves within the solid matrix. Linear instability analysis reveals that the inclusion of the Cattaneo effect induces oscillatory convection, in contrast to the stationary convection observed in its absence. The combined influences of the couple-stress parameter, interphase heat transfer coefficient, dimensionless solid thermal relaxation time, porosity-modified conductivity ratio, conductivity ratio, and the fluid's effective thermal diffusivity on system stability are systematically investigated. Critical stability parameters computed for aluminum oxide and copper oxide porous materials indicate that both the couple-stress parameter and the solid thermal relaxation time stabilize the onset of convection. A weakly nonlinear stability analysis based on a multi-scale method shows that the amplitude of linear wave motions, whether stationary or oscillatory, is governed by a first-order nonlinear evolution equation. The stationary mode may exhibit either supercritical or subcritical instability, depending on the governing parameters, whereas the overstable mode is exclusively supercritical. Notably, the transition from supercritical to subcritical instability occurs at lower interphase heat transfer coefficients for aluminum oxide porous media than for copper oxide. Overall, the results provide new physical insights into the interplay among couple-stress effects, solid thermal relaxation, conductivity ratios, the fluid's effective thermal diffusivity, and local thermal nonequilibrium effects on convection stability in porous media.</p>