The project is aimed to solving the fundamental scientific problem of the physics of nonequilibrium states associated with the experimental and theoretical study of the formation of micro- and nano-structures during phase transformations in spatially inhomogeneous conditions. An analogy between the evolution of phases during a first-order phase transition and the kinetics of a ferroelectric domain structure durin polarization reversal allows us to use uniaxial ferroelectric crystals of the KTiOPO4 potassium titanyl phosphate family (KTP) as a model materials. It should be noted that crystals of the KTP family are one of the main materials of nonlinear optics which can be used for creation of laser light frequency conversion devices using quasi-phase matchin. These are the only nonlinear optical crystals that are grown in Russia. To solve the stated problem, we will study experimentally and by computer modeling the evolution of the ferroelectric domain structure under both equilibrium and strongly nonequilibrium polarization switching conditions using single crystal plates of uniaxial ferroelectrics of potassium titanyl phosphate doped with Rb (Rb: KTP) and potassium titanium arsenate (KTA). The evolution of the domain structure in Rb: KTP and KTA single crystals has not been systematically studied yet. The domain structure visualization methods developed and successfully used for the crystals of the lithium niobate and lithium tantalate family and tested for KTP crystals were not used. An analysis of switching currents using the modified Kolmogorov-Avrami approach, which allows obtaining important statistical information on the kinetics of the domain structure, was not implemented. At the same time, Rb: KTP and KTA crystals can be used as model materials for studying the kinetics of the domain structure, since the method of their growth is quite well developed, which avoids the influence of defects and spatial inhomogeneity of the composition. These crystals have the same high values ​​of nonlinear optical coefficients as KTP crystals, but poses lower threshold fields and a larger optical damage threshold, which makes them attractive materials for creating the precision regular domain structures that are necessary for highly efficient laser frequency converters.