Universality of composite functions of periodic zeta functions

In the paper, we prove the universality, in the sense of Voronin, for some classes of composite functions F({zeta}(s;a)), where the function {zeta}(s;a) is defined by a Dirichlet series with periodic multiplicative coefficients. We also study the universality of functions of the form F({zeta}(s;a{sub 1}),...,{zeta}(s;a{sub r})). For example, it follows from general theorems that every linear combination of derivatives of the function {zeta}(s;a) and every linear combination of the functions {zeta}(s;a{sub 1}),...,{zeta}(s;a{sub r}) are universal. Bibliography: 18 titles.