A hypothesis is formulated and substantiated that quasi-static deformation in an amorphous metal alloy is a complex relaxation multi-stage process, which is a hierarchical sequence of interrelated structural transitions of the first order ordered in time. These nonequilibrium processes sequentially proceed at different scale space-time levels, starting from the lowest level --- a cluster of atoms of the first coordination sphere with a relaxation time taueta, then the middle level - a nanocluster of atoms of the fifth coordination sphere with a relaxation time tauφ, spatial scale of 10 nm and relaxation time tau, and tau>>tauφ>>taueta. They are accompanied by transformations of various types of potential energy of atoms (elastic, inelastic, plastic deformation, ZST) into each other. A mechanism and a model of a nonequilibrium transition from an elastic mechanical state to a state with shear transformation zones, a mechanism and a model of localized plastic deformation in an amorphous metal alloy are constructed. In the interval of non-uniqueness, in response to a locally introduced perturbation, a traveling autowave arises, which transfers the slip band from the inelastic deformation regime to the plastic deformation regime. Model parameters are estimated and important physical properties of plastic deformation are calculated. Keywords: Amorphous metal alloys, mechanical load, plastic deformation, nonequilibrium structural transition, synergetic model, kinetic equations, autowave.