This paper focuses on stock markets, including Portugal¡BItaly¡BIreland¡BGreece and Spain, and these are named PIGS by economists. Furthermore, we add the other three countries, U.S.A.¡BU.K. and Germany in this paper for investigating the dependence structure in the stock markets between these countries during the period 2001-2011. We implement a regime-switching copula model based on Gaussian copula, which uses a GARCH specification for the marginal distributions and the Gaussian copula for the joint distribution. Our method combines copulas and regime-switching models to demonstrate dependence sructures in stock markets between these countries. Based on this paper, we have two reports for international investors. First, if the dependency changes over time, the returns of portfolio diversification may be prone to diversification disasters, and the international investors' degrees of diversification can cause higher systemic risk in the period of financial crisis. Second, the phonomenon of the asymmetric dependence exists in financial markets, and we conclude that non-diversification may be better than diversification in the period of financial crisis.