  In this paper we analyze iterations of the obstacle problem for two different
operators. We solve iteratively the obstacle problem from above or below for
two different differential operators with obstacles given by the previous
functions in the iterative process. When we start the iterations with a super
or a subsolution of one of the operators this procedure generates two monotone
sequences of functions that we show that converge to a solution to the two
membranes problem for the two different operators. We perform our analysis in
both the variational and the viscosity settings.
