Superpositions (compositions) of multiplace functions have various applications in the modern mathematics, especially in the algebraic theory of automata [1], [3], [4]. It is known that any automaton with n entrances and m exits can be de_ned by some functions of the form f : An ! Am, which are called multiplace vector-valued functions. There are two types of compositions of such functions: serial ± and parallel ? which were considered by B. Schweizer and A. Sklar in [5], [6], [7]. In this paper we _nd the abstract characterization of algebras of the form (©; ±; ?;¢; F), where © is the set of multiplace vector-valued functions stable for compositions ± ; ? and containing two functions ¢(x) = x, F(x; y) = y. We also describe the case when © contains all vectorvalued functions de_ned on a _xed set A. Automorphisms of such algebra are described too.