1. Consider an equation Au = f, where A is a linear operator on a Hilbert space H. Suppose one can write A = Al + A2, where the operators Al and A2 satisfy certain conditions given below. Two theorems are proved showing that the solution u can be approximated arbitrarily closely by an iterative method which is analogous to the Peaceman-Rachford method for solving matrix equations. (See [1], [2]. The operators Al and A2 play the role of H and V in the Peaceman-Rachford method.) In particular the conditions are satisfied when A is the unbounded operator