This chapter develops a framework for analyzing the stochastic dynamics of small growing trading economies with CES sector technologies. The open neoclassical two-sector growth model with a diffusion process (uncertainty) for the aggregate saving/investment ratio is demonstrated with sample paths and long-run probability distributions of the overall factor endowment ratio. Stochastic endogenous growth and cycles require a combination of fundamental growth parameter values: saving rates, terms of trade, and sectorial substitution elasticities. It defines and demonstrates the conditions for full and partial specialization, under consideration of the factor reversal effects of the CES technology. With this theoretical background, it solves the same model under uncertainty, and it illustrates the regions within the parameter space that include parametric values generating nonstationary sample paths of stochastic endogenous growth and cycles. The chapter finally compares the results and the expectations of the stochastic model with those of its deterministic counterpart, which serves indeed as the economic benchmark.