We describe analytically the relaxation process of Brownian motion of rotators subjected to external field E, which is suddenly switched on at time t=0. The field E is constant, E=E(0), or time dependent, E=E(0) sin omega t. We make detailed calculations, respectively, for one dipole in the field E and two interacting dipoles in the field E. However, the method involving any finite number of rotators is described. In particular, we derive analytical formulas for the first dipole moment and compare the numerical results with the computer experiment.