  We study the two membranes problem for different operators, possibly
nonlocal. We prove a general result about the H\"older continuity of the
solutions and we develop a viscosity solution approach to this problem. Then we
obtain $C^{1,\gamma}$ regularity of the solutions provided that the orders of
the two operators are different. In the special case when one operator
coincides with the fractional Laplacian, we obtain the optimal regularity and a
characterization of the free boundary.
