The effect of time-periodic boundary temperatures on the onset of double diffusive convection in a fluid-saturated anisotropic porous medium is studied by making a linear stability analysis. A perturbation method based on small amplitude of the imposed temperature modulation is used to compute the critical values of thermal Rayleigh number and wave number. The correction thermal Rayleigh number is calculated as a function of frequency of modulation, viscosity ratio, anisotropy parameter, porous parameter, Prandtl number, diffusivity ratio and solute Rayleigh number. The effect of various physical parameters is found to be significant at moderate values of the frequency. We found that it is possible to advance or delay the onset of double diffusive convection by proper tuning of the frequency of modulation of the wall temperature. The effect of various parameters on the stability of the system is brought out. (C) 2003 Elsevier Ltd. All rights reserved.