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Natural convection in a cube of fluid-saturated porous medium having a constant temperature top and bottom is studied numerically. In the first of two special cases considered, the vertical sides are insulated. In this case, the numerical simulations indicate permanently unsteady regularly and irregularly fluctuating convective states at Rayleigh numbers (R*) above 550. The regularly fluctuating convective state defined by simply periodic oscillations in the Nusselt number begins at R* between 550 and 560. The frequency of the oscillations appears to depend on R* approximately as f∝ (R*)3.6. The irregularly fluctuating convective state defined by random variations in the Nusselt number begins at R* between 625 and 640. In the second case, heat is transferred through the vertical sides of the cube. Three distinct flow patterns are identified depending on the rate of heat transfer and the Rayleigh number. For all runs in the range of Rayleigh numbers studied, the transition from the first to the second flow pattern occurs abruptly.