In this paper, we present a new kind of ABS methods, called row update ABS methods, for solving systems of nonlinear equations. We use the previous function values to approximate derivatives of functions in some sense. Onlyncomponent function evaluations at each iteration are needed and no derivatives of functions are involved. Under some mild assumptions, we prove that the row update ABS methods are locally and superlinearly convergent. A numerical comparison with Newton's method, Brqyden's method and the original ABS methods is also given, showing that the new methods are competitive with other methods. AMS Subject Classification:65H10