An extension of algorithmic logic is considered, i.e., a program substitution operator is introduced. For three different algorithmic logics (original with iterative quantifiers, extended with classical quantifiers and nondeterministic) it is proved that program substitution does not lead outside the provable formulae. If the substitution rule is introduced to the inference rules of original algorithmic logic, then the consequence relation is algorithmically structurally complete. For extended algorithmic logics this question is open.