In his paper [6], M. Steurich introduced the notion of the semigraded local ring as a generalized concept of a power series ring over a field. Corresponding to the non-homogeneous case, we investigate in this paper, how the properties of Golod homomorphisms, due to G. Levin [3], can be transfered to the semigraded case. And, by making use of it, we obtain some change of ring theorems about Poincare series in our semigraded case. Throughout the paper, all rings are commutative and Noetherian, and the symbol (R, m, k) stands for R is a local ring with maximal ideal m and residue field k
