This paper aims to investigate the possible linkage and non-linear interaction between crude oil and stock markets using cointegration and causality tests. Daily data on world crude oil prices and the stock indices of Japan, Taiwan, South Korea, Australia, Indonesia, India, Singapore and Malaysia are selected for this study. Unlike the previous literature, by conducting a non-linear cointegration analysis, we obtain evidence of non-linear long-term equilibrium between crude oil and stock markets for the eight Asia-Pacific markets. The Granger causality tests demonstrate the existence of bidirectional short-run Granger causality between crude oil and these Asia-Pacific stock markets. The long-run Granger causality between them is unidirectional. However, the speed of adjustment toward long-run equilibrium is relatively slow.