This paper investigates asymmetric increasing trends in dependence in major international equity markets. To this end, we develop a multiple-regime smooth-transition copula GARCH model and address several important questions, including the number of regimes and the existence of increasing asymmetric trends in dependence. Our results suggest that two or three regimes are sufficient for describing the dependence trends in international equity markets over the last 35 years with significant asymmetric increases. In addition, the implied time-series of three dependence measures show a wide variety of dynamics, demonstrating the usefulness of our framework to describe asymmetric increasing dependence trends. Finally, we evaluate the economic significance of our empirical finding based on the 99% value at risk and expected shortfall. Our result indicates that both risk measures have increased approximately 20% over the last 35 years in major equity markets.