Abstract: The topological degree theory has important value in the sense that it gives information about the number of distinct solutions,continuous families of solutions and stability of solutions1.Recently,the solvability of the operator equation y∈(A+C)x was discussed by means of topological degree theory2,3.In this paper,a generalized degree for maccretive operator A perturbed by condensing mapping C is established,and an useful tool for solving the operator equation y∈(A+C)x is supplied.