Uncertainties are intrinsic features of dynamic economic systems, and this chapter considers the dynamic implications of factor endowment (labor, capital) uncertainties for a small growing trading economy. Our stochastic growth models extend the open neoclassical two-sector growth model to a stochastic environment in continuous time and extend the diffusion dynamics of one-sector growth models to a trading two-sector economy. We demonstrate that the basic propositions of deterministic steady-state growth and endogenous growth theory, under some specifications and certain parametric restrictions, are preserved within a stochastic framework.