Numerical simulations of two-phase Rayleigh-Bénard convection in a cylindrical cell with particles or vapor bubbles suspended in the fluid are described. The particles or bubbles are modeled as points, the Rayleigh number is 2×106 and the fluids considered are air, for the particle case, and saturated water for bubbles. It is shown that the presence of a second phase has a profound effect on the flow and heat transfer in the cell. The heat capacity of the particles and the latent heat of the liquid are used, in dimensionless form, as control parameters to modulate these effects. It is shown that, as these parameters are varied, the nature of the flow in the cell changes substantially, in some cases with adverse and in others beneficial effects on the Nusselt number. By the analysis of several aspects of the numerical results, a physical discussion of several mechanisms is provided.