In order to investigate the transport processes of carriers in the amorphous semiconductor superlattices, we have proposed and rigorously solved the continuous-time random walk model in the form of superlattice for the migration of carriers. Being based upon this, the generalized form of the Pick's law in these materials has been obtained, and the mobility of carriers, varying with the frequency and the modulation wavelength, has been calculated for the Gaussian and non-Gaussian time-distribution functions respectively. It has been shown that the long-time-tail behaviour (for the non-Gaussian distribution) may partly cancel the size-effect due to the structural modulation.