Most studies of business cycle exclude the dimension of asymmetric conditional volatility. In this paper, we propose three bivariate asymmetric GARCH models to capture the properties of conditional volatility and time-varying conditional correlations of business cycle indicators in four OECD countries. Our study extends the constant conditional correlation framework proposed by Bollerslev (1990) and the time-varying conditional correlation approach by Tse and Tsui (2002), respectively. Using indices of industrial production as proxies for business cycles indicators, we detect statistically significant evidence of asymmetric conditional volatility in the UK and US. Additionally, we find that the conditional correlations are significantly time-varying, and that the strength of varying correlations may be linked to the degree of economic integration between the countries.