This paper adopts a bivariate ABEKK GARCH-X-t model to examine the bilateral relationships between the Shanghai A- and B-shares stock markets in China by using daily data of the markets. One-way mean spillover is detected from A-shares to B-shares stock market for the period of study. Good and bad news affect the volatility of the A- and B-shares markets unequally. In addition, there is evidence that the change in conditional correlations may be due to the opening of B-shares to Chinese citizens and has connection with market information arrival. Furthermore, the change in conditional correlations may have investment implication on asset allocation.