In this paper are investigated a polynomial formal group analogues of the operators introduced by Coleman for the Lubin Tate formal group and the multiplicative formal group. Explicit constructions of the norm and trace operators for Laurent series are given, their main propirtes are checked. The eigenvalues and root values of these operators are also studied, and a homomorphism is constructed that connects the additive structure and the structure of the formal module on the set of formal power series.