A generalized version of the Zel'dovich approximation which is applica
ble in both the radiation-dominated and the matter-dominated epochs is
presented. This approximation allows one to follow the growth of inho
mogeneities from the time the mode enters the Hubble radius until it t
urns around. Comparison of the results with the standard spherical mod
el shows that the analytic approximation is quite good even in the non
linear regime. Detailed application to cold dark matter models and see
ded models are given.