Since the work of Michaud (1970), the abundance anomalies observed in the peculiar Ap and Am stars are increasingly believed to be a consequence of diffusion processes in stellar atmospheres or stellar envelopes. A number of the problems that seemed at first sight insoluble within the framework of diffusion processes have now been solved by it. Diffusion processes can, for example, account for anonalous helium isotopic ratios (Vauclair et al, 1974 (b)) and mercury isotopic ratios (Michaud et al, 1974). Quantitative results on abundance variations due to diffusion processes have been obtained (Michaud et al, 1976; Michaud, this conference; Alecian, 1976). They show that, in general, the relative abundance anomalies obtained from computation are close to the observed ones. It is now well established that the largest abundance anomalies observed in Ap stars (for rare earths) can be interpreted by diffusion processes with a satisfactory time scale, in a completely stable atmosphere. However, the predicted absolute abundance variations often exceed the observed ones, as in the case of Am stars. This suggests that the assumption of stability is not completely valid for the stellar gas: some kind of macroscopic motion, such as a meridional circulation or turbulence or both, must be at work and slow down the diffusion.