If a group G is presented in terms of generators and relations, then the classical Reidemeister-Schreier Theorem  gives a presentation for any subgroup of G. If G is a free product of groups Gα each of which is presented in terms of generators and relations, then the main result of this paper is a presentation for any subgroup H of G, which shows the nature of H as a free product of certain subgroups of G. This result is a generalization of the celebrated Kuroš Theorem . It also includes the Reidemeister–Schreier Theorem and the Schreier Theorem  which states that any subgroup of a free group is free.
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