In this paper we show the results of some research carried out on parallel iterative methods to solve equations. In particular we study general classes of one point parallel methods and multipoint ones without memory, and we point out the convergence order of these methods and the conditions which are both necessary and sufficient for them to be optimal. In addition we prove that the convergence order for multipoint parallel procedures without memory cannot be more thenr(r+)m−1, wherer indicates the number of the parallel processor used andm the number of the functions and eventual derivatives, calculated not simultaneously in every iteration.