During the past few years, many of the financial markets have gone through devastating effects due to the crisis in one or the other economy of the world. The recent global financial crisis has triggered dramatic movements in various stock markets which may arise from interdependence or contagion between the markets. This article attempts to measure the contagion between the equity markets of Asia and the US stock market. The countries considered in the Asian group are China, India, Indonesia, South Korea, Taiwan, Hong Kong, Malaysia and Japan. Most of the Asian economies have experienced drastic higher volatility and uncertainty in the financial markets. If the markets are contagious, then the investors will be unable to reap benefits through international diversification of the portfolio. In such a case, the policymakers will further frame policies so that they can insulate themselves from inflicting heavy damage from various crises. To achieve our goal, we make use of the time-varying copula approach which helps us to study the joint behaviour of the series based on their marginal distribution. Time-varying copula approach can also capture the non-linear dependence in the series and exhibits a rich pattern of tail behaviour. Our findings support the contagion between the Asian stock markets and the US stock market during the global financial crisis. This article also highlights that the increased tail dependence is an important factor for the contagion between the Asian stock markets and the US market.