It is known that the domestic and the U.S. stock prices tend to move together as those markets are closely interrelated. In this study, cointegration and causal relationships among the four stock price indexes of KOSPI, KOSDAQ, DOWJONES and NASDAQ are carefully investigated for the period of declining stock prices in the long run. When all indexes move in a similar fashion, cointegration does not exist and the causal linkages between the domestic and the U.S. stock prices appear relatively complex. On the other hand, when the domestic and the V.S. stock prices move in a different manner, cointegration exists and the causal relationships appear relatively simple. NASDAQ is apparently found to lead the domestic stock market in both periods, which is consistent with the actual market situation when the If industry is under recession.