Horizontally layered structures can develop in porous or partially molten environments, such as magma chambers, the early Earth's mantle, and hydrothermal systems. We have studied the generation and evolution of these horizontally layered structures in a rigid porous medium by heating a compositionally stably stratified fluid from below. Growth of a convective layer through entrainment, the formation of a vertical density interface on top of this layer and destabilization of the next layer are closely coupled. It is shown that the growth of the first convective layer stops once the thermal equilibrium is reached. Since heat (solute) transfer across the thin density interfaces becomes purely diffusive (dispersive), the separately convecting layers can persist on a compositionally dispersive timescale. While the number of layers that develop is determined by the magnitude of the thermal Rayleigh number, the final height of a newly formed layer is inversely proportional to the buoyancy ratio. Two dynamical mechanisms which lead to sudden interface disappearance determine the vertical layer scales, rather than the initial evolution toward the thermal equilibrium. Finally, the results are discussed with respect to the above mentioned geophysical scenarios. ¿ 1998 American Geophysical Union