Based on a system of evolutionary equations for an ensemble of edge dislocations, the problem associated with the development of instability of a homogeneous distribution of dislocations is considered. Despite the large number of theoretical studies on this topic, most of them are considered within the framework of reaction-diffusion phenomenological models, which contradicts the mathematical structure of the initial evolutionary equations, which are hyperbolic equations. For the initial system of hyperbolic equations, the case is considered when the process of plastic deformation develops along a given axis. The elastic interaction of dislocations is neglected in order to reveal the instability features of the homogeneous state of the system due to the local kinetics of dislocations. The stability analysis of the homogeneous state was carried out for a system of dislocations of two types differing in mobility. As a result of linearization of the initial system, a system of homogeneous linear algebraic equations is obtained. From the condition of the existence of its nontrivial solutions, a dispersion equation is found, using which, on the basis of the Raut – Hurwitz criterion, the range of parameters of the initial system at which kinetic instability is realized is established. In the instability region, an expression is obtained for the increment of the unstable mode, which determines the behavior of the system beyond the bifurcation point, and an expression for the characteristic scale of the inhomogeneous structure. The region of system parameters where the diffusion dynamics of the system is realized is found. It is shown that the Turing instability for the total dislocation density is realized in this parameter range. Within the framework of the initial system of hyperbolic equations, the dynamics of both total and excess dislocation densities is significant. It is the excess density that leads to disorientation in the formation of heterogeneous dislocation structures. This is a fundamental point, since at the advanced stage of plastic deformation, the dislocation structure is basically a system of disoriented cells and ragged sub-boundaries.