This paper develops optimal tests based on sequential predictive moment conditions. We show that an appropriate weighting version of the predictive test achieves the same power as optimal structural change tests proposed by Sowell (1996a) Optimal tests for parameter instability in the generalized method of moments framework. Econometrica64:1085-1107 and (1996b) Tests for Violations of MOMENT conditions. Manuscript.Graduate School of Industrial Administration, Carnegie Mellon University. Consequently, we can apply directly Sowell's results. Optimal predictive tests for parameter instability and overidentifying restriction stability are proposed. The finite sample properties of LM, Wald, LR-type and predictive tests for parameter instability are studied via a simulation study.