This paper considers certain questions related to application of multilevel mathematical models for description of processes of severe inelastic deformations of monocrystals and polycrystals that require usage of geometrically and physically nonlinear constitutive relations. The scope of consideration includes the questions related to application of multilevel models of inelastic deformation of monocrystals and polycrystals developed based on crystal plasticity, in order to describe experimentally known effects that arise under the complex loading. Study of the two-level model of inelastic deformation of polycrystalline metals the consideration of the effects of scalar and vector properties delay, verification of isotropy postulate and proposition of possible explanation from physical positions of the effect of lagging of vector properties are studied. We also introduce the parameters characterizing the accumulation of damage and formulate fracture criterion using methodology of multilevel modelling.