In this paper, we examine a conditional version of the international capital asset pricing model (ICAPM) allowing for a time and state varying factor of proportionality or beta. Betas are allowed to change with an unobserved state variable. Return variances differ across the different states so that betas differ on account of differences in variance regimes of the return series. This method allows us to accommodate a non-linear relationship between returns and variances. For six markets, we find that the world beta is a non-linear function of domestic volatility. In the Pacific and North American markets, we find strong evidence for a time and state varying beta coefficient. We find that for the European markets, with the exception of Switzerland, the world beta is not related to the state of the domestic market's volatility.