The results of two-dimensional simulations of the deep circulation of Venus are presented. They prove that the high surface temperature can only be explained by the greenhouse effect, and that Goody and Robinson's dynamical model is not valid. Very long time integrations, up to a time comparable with the radiative relaxation time, confirm these results. Analytical radiative equilibrium solutions for a semi-grey atmosphere, both with and without an internal heat source, are presented. It is shown that the green-house effect is sufficient to produce the high surface temperature if τT* ≫ 100 and S = τS*/τT* ≲ 0.005. This result is still valid in the presence of an internal heat source of intensity compatible with observations. A two-dimensional version of a three-dimensional model is used to test the validity of the new mechanism proposed by Gierasch to explain the 4-day circulation. Numerical experiments with horizontal viscosities vH = 1011 – 1012 cm2 s−1 failed to show strong zonal velocities even for the case of large Prandtl numbers. It is observed that the dissipation of angular momentum introduced by the strong horizontal diffusion more than compensates for the upward transport of angular momentum due to the Hadley cell. Preliminary three-dimensional calculations show a tendency to develop strong small-scale circulations.