  We introduce the notion of composite growth function and provide examples
that illustrate the primary properties of these growth functions. There are
provided examples of Mealy automata that have composite non-monotonic growth
functions of the polynomial growth order. There are described examples of Mealy
automata that have composite monotonic growth functions of intermediate and
exponential growth. The questions concerning the interrelation between the
notions ``composite'' and ``non-monotonic'' of a Mealy automaton growth
function are formulated.
