Linear and weakly nonlinear properties of Rayleigh-Benard convection in rotating fluids are investigated. Linear stability analysis is studied to investigate analytically the effect of Coriolis force on gravity-driven convection for idealised stress-free boundary conditions. We have derived a nonlinear one-dimensional Landau-Ginzburg equation with real coefficients near the onset of stationary convection at the supercritical pitchfork bifurcation. A coupled Landau-Ginzburg type equations with complex coefficients near the onset of oscillatory convection at the supercritical Hopf bifurcation are derived and discussed the stability regions of travelling and standing waves. (C) 2007 Published by Elsevier Ltd.