The planning of offshore oil or gas field infrastructure under uncertainty is addressed in this article. The main uncertainties considered are in the initial maximum oil or gas flowrate, the recoverable oil or gas volume, and the water breakthrough time of the reservoir, which are represented by discrete distributions. Furthermore, it is assumed that these uncertainties are not immediately realized, but are gradually revealed as a function of design and operation decisions. To account for these decision-dependent uncertainties, we propose a multistage stochastic programming model that captures the complex economic objectives and nonlinear reservoir behavior and simultaneously optimizes the investment and operating decisions over the entire planning horizon. The proposed solution algorithm relies on a duality-based branch-and-bound method involving subproblems as nonconvex mixed-integer nonlinear programs. Several examples involving nonlinear reservoir models are presented to illustrate the application of the proposed method.