It is shown that discontinuities corresponding to points of certain quasitransverse shocks, that are not evolutionary from cuts of the shock adiabat, in an isotropic prestressed elastic medium are a sequence of two evolutionary shocks moving at identical velocity. Two such representations are obtained for certain sections of the shock adiabat. The possibility of representing the non-evolutionary discontinuities in the form of a sequence of evolutionary discontinuities moving at identical velocity in other problems of the mechanics of a continuous medium is discussed. Quasitransverse shocks are investigated below within the framework of the approximations made in /1,2/, where the set of states (the shock adiabat), into which it is possible to drop from a given initial state by a jump while conserving the conservation laws, was investigated for lowintensity shocks. Segments satisfying the condition of no decrease in entropy and the evolution conditions, i.e., the necessary conditions for correctness of the linearized boundary conditions on the discontinuity /3/, were extracted on the curve representing the shock adiabat. Discontinuities corresponding to shock adiabat segments satisfying the requirement of no entropy decrease but not satisfying the evolutionarity conditions because of an excess in the number of boundary conditions over the number of unknowns in the linèarized problem of interation between small perturbations and the discontinuity, are discussed in the present paper. Representation of the non-evolutionary discontinuities in the form of a sequence of evolutionary discontinuities moving at one velocity can turn out to be useful in solving different selfsimilar problems containing discontinuities.