Modeling the dependency between stock-market returns is a difficult task when returns follow a complicated dynamics. When returns are non-normal, it is often simply impossible to specify the multivariate distribution relating two or more return series. In this context, we propose a new methodology based on copula functions, which consists in estimating first the univariate distributions and then the joining distribution. In such a context, the dependency parameter can easily be rendered conditional and time-varying. We apply this methodology to the daily returns of four major stock markets. Our results suggest that conditional dependency depends on past realizations for European market pairs only. For these markets, dependency is found to be more widely affected when returns move in the same direction than when they move in opposite direction. Modeling the dynamics of the dependency parameter also suggests that dependency is higher and more persistent between European stock markets.