We study the existence of dynamic equilibria with endogenously complete markets in continuous-time, heterogenous agents economies driven by diffusion processes. Our main results show that under appropriate conditions on the transition density of the state variables, market completeness can be deduced from the primitives of the economy. In particular, we prove that a sufficient condition for market completeness is that the volatility of dividends be invertible and provide higher order conditions that apply when this condition fails as is the case in the presence of fixed income securities. In contrast to previous research, our formulation does not require that securities pay terminal dividends, and thus allows for both finite and infinite horizon economies.