Modeling the dependency between stock market returns is a difficult task when returns follow a com-plicated 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 distri-bution. 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 con-ditional dependency depends on past realizations for European market pairs only. For these markets, de-pendency is found to be more widely affected when returns move in the same direction than when they move in opposite directions. Modeling the dynamics of the dependency parameter also suggests that de-pendency is higher and more persistent between European stock markets.