Abstract: In Reference literature[1], it is easier to obtain the solutions to, initialboundary value problems of some partial defferential equations by. using an operator series method. In this paper, we extend the results in[1]to more general cases so that we can make use of the operator series method to solve much more determined-solution problems(such as Cauchy problems of differential and differential-integral equations,semi-unbounded problems, initalboundary value problems and so on).