Based on Markov switching dynamic conditional correlation (MS-DCC) and independent switching DCC (IS-DCC) models，we construct a Markov independent switching DCC (MIS-DCC) model which has the advantage to be estimated and analyzed accurately． Then we investigate the contagion effects among five major stock markets from the American subprime mortgage crisis to European sovereign debt crisis． We find that， firstly，our model endogenously characterizes different intervals of the contagion，which effectively avoids the shortcoming that divides the whole sample into pre-crisis and post-crisis period arbitrarily． Secondly，we find it is necessary for countries to cooperate with each other to respond to crises since American subprime mortgage crisis and European sovereign crisis evolve into a systemic risk． Thirdly，there is the evidence that America and other relevant countries miss the time to respond to the American subprime mortgage crisis． Fourthly，we find more complex information in period of the crisis，which results to frequently switch between different regimes of the market． Finally，both conditional and unconditional correlations can be described intuitively by regime variables．