Simultaneous equations models of economic processes may deliver multiple, single or no solution. This is an important econometric issue in nonlinear models and has received particular attention in econometric models involving discrete outcomes. In this research we develop an unifying framework within which identification issues can be studied. We develop sharp identified sets for structural functions and distributions of latent variables under a variety of assumptions concerning the way in which processes are observed. Applications include the simultaneous market entry game studied in empirical industrial organisation.