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The main objective of the paper is the investigation of adiabatic shear band localization phenomena in inelastic single crystals under dynamic loading processes. In the first part, a rate-dependent plastic model of single crystals is developed within the thermodynamic framework of the rate-type covariance constitutive structure. This model takes account of the effects as follows; (i) influence of covariance terms, lattice rotations and plastic spin; (ii) thermomechanical coupling; (iii) evolution of the dislocation substructure. An adiabatic process is formulated and examined. The relaxation time is used as a regularization parameter. The viscoplastic regularization assures the stable integration algorithm by using the finite element method. It has been shown that the evolution problem (the initial-boundary value problem) for rate-dependent plastic model of single crystals is well posed. The second part is devoted to the investigation of criteria of localization of plastic deformation in both single slip and symmetric double slip processes. The adiabatic shear band formation in elastic-plastic rate-independent single crystals during dynamic loading processes is investigated. The critical value of the strain hardening rate and the misalignment of the shear band from the active slip systems in the crystal's matrix have been determined. Particular attention is focused on the investigation of synergetic effects. Calculations have been obtained for aluminum single crystals. The results obtained are compared with available experimental observations.