As unit root and cointegration theories are applied to the long-run time series, it is increasingly interested in the possibility of the structural change in the long-run relationship of the related variables for the sample period. Changes in economic conditions in the past suggest the possibility of thestructural break in the long-run equilibrium between the stock and related markets, thus conventional time-invariant cointegration tests are not likely to be effective. This study explicitly investigates the characteristics of the long-run structural mechanism and the dynamic stability of the domestic stockmarket system from the time-variant and the time-invariant viewpionts. Residual based tests for cointegration that allow for the possibility of structural break indicate a stable, but time-varying, long-run equilibrium between the markets. Test statistics for parameter stability characterize the cointegrating relations as stable but gradually evolving random walk process. When the short-run adjustment process is included in testing the stability, the long-run relation turns out to be stable while the short-run relation is unstable. Hence the statistical tests consistently demonstrate the stable cointegrating relation, with slightly time-variant effect, in the domestic stock market system.