Intertemporal caital asset pricing and the stochastic properties of optimal portfolios and consumption are examined in a countinuous-time recursive utility (stochastic differential utility) model with multiple state variables dynamically affecting investment opportunities. Although Merton-Rechard’s multi-beta intertemporal CAPM (ICAPM) relationships are valid, they do not collapse to the consumption-based single beta CAPM (ICAPM). Instead, several multi-beta versions of CCAPM are proposed in both heterogeneous and homogeneous agents settings. The multiple correlation coefficient of the individual agent’s optimal consumption with the aggregate consumption and multiple state variables is unity.