This paper investigates the partial adjustment process with asymmetries and spillovers on stock index returns of Hong Kong and China. The empirical evidence shows that index returns do have asymmetric adjustment behaviors in most of markets except the A-share market in Shenzhen. On the other hand, the volatility shows stronger asymmetric adjustment behavior than returns, which implies information innovations influence the information absorption process regardless of information contents. As for the spillover effects, we find that past returns of security markets on China generally have no impacts on Hong Kong market except the concurrent impact of the B-share market in Shanghai. The past returns of Hong Kong market, however, do have strong impacts on the B-share market in Shanghai. This suggests the significant cross-correlation between the B-share market in Shanghai and Hong Kong market.