The review is concerned with studies of transformation of various types of atomic order during its relaxation from non-equilibrium state to equilibrium one and determination of microscopic parameters of migration of atoms, which characterize such relaxation in solid solutions (such as f.c.c.-Ni—Al alloys and $С32$-(Ti,W)B$_{2}$ crystalline compounds). Forecasted temperature dependences of residual electrical resistance of equilibrium f.c.c.-Ni—Al solutions are considered. Parameterization of the abnormal behaviour of kinetics of residual electrical resistance of f.c.c.-Ni—Al solutions is carried out. Results of investigation of a relaxation of distribution of diffuse-scattering intensity (over reciprocal space) caused by interatomic correlations for the single-crystalline samples of f.c.c.-Ni—Al solutions show that the structure of atomic order is characterised by a set of wave vectors including vector corresponding to $L1_{2}$-Ni$_{3}$Al- and $L1_{0}$-Ni$_{2}$Al$_{2}$-type ordered structures. Order parameters for different reference states and temperatures of their relaxation are estimated. The semi-phenomenological schema of estimation of (self)diffusion coefficients and activation energies of migration of atoms in binary solid solutions based on the Bravais lattices is modified for simple hexagonal lattices. Possible types of superstructures on an interstitial hexagonal sublattice in crystalline $С32$-(Ti,W)B$_{2}$ compound are predicted, and conditions of low-temperature stability of such structures arising from disordered arrangement of atoms of nonstoichiometric metal subsystem, depending on character of interatomic interactions in a few first coordination shells of a hexagonal sublattice are ascertained.