In this paper, we test the international conditional CAPM model of Dumas and Solnik (1993) and the international conditional APT model of Ferson and Harvey (1992), as well as various extensions of these models. These models were typically estimated by GMM and found to be valid according to the standard J-test. Given to the low power of J-tests against many specific alternatives, we propose several diagnostics to further scrutinize the empirical fit of these models. We show that although they could not be rejected on the basis of the overidentifying restrictions test, they are not very useful for consistently predicting the conditional first and second moments of equity and foreign exchange returns over time. Our specification search leads us to an alternative international conditional CAPM model with a factor ARCH formulation for modelling international returns for which we find strong support, both with the J-statistic criterion, as well as a number of other diagnostics tests, including tests for parameter stability, orthogonality of residuals and explicit analysis of pricing errors.