The onset conditions and the behavior of the developed secondary flow were investigated for double-diffusive convection in a horizontal layer of porous medium. The work concentrated on the case in which the layer is heated from below and saturated with a fluid having a stabilizing concentration gradient. Because the component with the larger diffusivity (heat) is destabilizing and the component with the smaller diffusivity (solute) is stabilizing, the motion at onset is predicted to be oscillatory according to linear stability theory. Experiments were conducted in a rectangular tank 24 cm long x 12 cm wide x 4 cm deep filled with glass beads 3 mm in diameter. The saturating fluid was distilled water and NaCl was the solute. The basic state salinity profiles were slowly diffusing in time, because the salt concentration was not maintained fixed at the solid top and bottom boundaries. Sustained oscillations were not detected at onset in the experiments; instead, there was a dramatic increase in the heat flux at the critical temperature difference. After more than one thermal diffusion time, the heat flux reached a steady value, which increased monotonically if the temperature difference was increased further. When the temperature difference was reduced, the heat flux exhibited hysteresis. Flow visualization indicated that the convection pattern of the developed flow was three-dimensional. In order to better model the experiments, linear theory was extended to include the effects of temperature-dependent thermal expansion coefficient and viscosity for water and the actual solute boundary conditions in the experiment. These extensions of the linear theory required numerical solution procedures. In addition, nonlinear solutions were obtained using finite differences, assuming the problem is two-dimensional. In the nonlinear calculations, the oscillatory motion predicted by linear theory was found to be unstable at finite amplitude. The breakdown of the initial oscillatory motion is followed by a large increase in the heat transport, similar to what was observed in the experiments. Both steady and oscillatory nonlinear asymptotic solutions were found, depending on the governing parameter values. Hysteresis in the heat curve was also obtained.