  In the present work we show that the Dirichlet series with the Euler product
having analytical continuation to the critical strip without singularities, in
some natural conditions, can be approximated by partial products of Euler type
in the critical strip, if the primes over which are taken the products are
distributed by a suitable way. The family of such series includes many of
widely used Dirichlet series as the zeta-function, Dirichlet L-functions and
etc. As a consequence the analog of the Riemann Hypothesis for such series is
proven.
