The intention of the present work is to evaluate long-run relations in the stock markets of six Latin American countries (Argentina, Brazil, Chile, Colombia, Mexico and Peru) and the United States stock market, by means of a model in which a cointegration relation exists between the principals prices stock indexes but allowing that the movements towards the long-run equilibrium only happen in some periods. For the previous thing threshold autoregressive models are considered. The idea is that the movements towards the long-run equilibrium need not occur every period but in a specific regime. We find that the specification is better in nonlinear than linear models and the cointegration relation only appears in four of the six analyzed Latin American countries.