In this paper the notion of factorization of functions with respect to contour Г in the spacesLp(Г; _) is presented [1]. The main result of the paper is the determination of some classes of functions that allow a factorization, as well as the application of factorization in studying of singular integral operators with measurable and bounded coe_cients. Let Г be a closed Lyapunov contour which bounds the domain G+: By GГ we denote the domainwhich complements G S Г to the whole plane. Assume that 0 2 G+ and 1 2 GГ: Let L+p (Г; _) = P(GLp(Г; _)); LГp (Г; _) = Q(GLp(Г; _)) + c; c 2 C: De_nition. The generalizedfactorization of function a 2 GL1(Г) with respect to contour Г in the space Lp(Г; _) is its representation in the form a(t) = aГ(t)t_a+(t); where _ 2 Z and the factors a_ satisfy the follwing conditions.