A family of SOP-secant methods for solving large-scale nonlinear systems of equations is introduced. The components and the variables of the system are divided into m blocks. At each cycle of the method, the groups of components ace changed one at a time using a quasi-Newton (least-change secant) step. Proofs of local convergence at an ideal rate are given, which use the theory of fixed-point quasi-Newton methods [J.M. Martinez, SIAM J. Numer. Anal., 29 (1992), pp. 1413-1434]. Numerical experiments are presented.311217226