Number of engineering systems can be characterized as complex since they have a dynamic and nonlinear behaviour incorporating a stochastic uncertainty. On the other hand, as a machine learning method, Gaussian processes (GP) provide a practical, probabilistic approach to learning in kernel machines. This makes them very suitable for obtaining probabilistic, nonparametric black-box models of stochastic nonlinear dynamic systems. In this paper, a novel study on the modeling and adaptive optimal control of a tubular reactor is made by using Gaussian processes. Such reactor is a typical example of a nonlinear distributed parameters system, whose first-principles dynamic models consists of partial differential equations. The purpose is to obtain a nonlinear autoregressive models with exogenous input (NARX) of the output concentration and temperature of the reactor by applying a GP modeling approach. The identified surrogate models are then used to design an adaptive model predictive controller to achieve optimal performance of the reactor despite of the stochastic changes in the feed temperature. The performance of the adaptive MPC based on GP models is studied by simulation experiments.