**Lacunary Analogs of the Runge Theorem
and Multiply **T**-universal Functions Representable by Lacunary Power Series in
the Space of Holomorphic Functions**

In this paper multiply T-universal functions representable by lacunary power series are investigated. Under general assumptions on a domain of holomorphi it is proved that the set of all such type functions is dense in corresponding subspace of holomorphic functions (theorems 3-5). The proofs are based on new results on possibility of uniform approximation by lacunary polynomials.