Spin dynamics of electrons in semiconductors and structures with quantum wells under conditions where pumping and probing are performed in the form of a periodical series of pulses is theoretically studied. It is shown that, at a fixed delay between the pump and probe pulses, the signal of spin amplification as a function of the magnetic field consists of a series of narrow peaks conditioned by commensurability of the period of spin precession and pulse repetition interval. In the case of anisotropic spin relaxation, the peak centered at the zero magnetic field is suppressed compared with the neighboring peaks. The role of inhomogeneous broadening of the frequency of the Larmor precession in the formation of the spin amplification signal is analyzed.