Ever-increasing attention to the investigation of nondeterministic processes that generalize deterministic processes because of elimination of the rigidity of execution inherent in the latter is characteristic of modern programming. Nondeterminism reflects the crux of the sampling problem in tasks allowing multivaluedness of solutions such as automation of the proofs of theorems, syntactical and semantical models of languages, distribution of resources in multiprocessor computer systems and time-sharing systems, etc. Nondeterminism is used in proving any assertions about programs by means of the apparatus of program logic that occur and are developed on the junction of mathematical logic and the theory of programming. The systems of algorithmic algebras (SAA) proposed by Glushkov (1956) and adequate conceptions of structural programming are the fundamental basis of propositional program logic. In the interests of orientating the SAA apparatus in the formalization of parallel calculations, their signature was expanded by including filtration and parallelism operations. The algebraic systems obtained in this manner were called modified SAA. Identity problems and axiomatization by using a single deduction rule, the traditional formulation, were solved by Tseitlin (1974) for s(o)-algebras modified by SAA with closed logic conditions. In this paper, the mentioned results are extended to the case of s(h)more » algebras, SAA with closed logic conditions, in whose signature the parallelism operations are replaced by nondeterministic disjunction operators. 9 references.« less