Convergence of general iteration methods for linear operator equations are investigated in a limit space. If the equation is not solvable, the iterates converge to a generalized solution. If the equation is not uniquely solvable, the initial approximation can be chosen in such a way that the iterates converge to an arbitrary solution. Furthermore, the iteration method yields the inner inverse of the operator. The article generalizes results of G. Mae3 [8] for linear systems of equations with rectangular matrices.