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This paper introduces a methodology for the reliability-based design optimization of systems with nonlinear aeroelastic constraints. The approach is based on the construction of explicit flutter and subcritical limit cycle oscillation boundaries in terms of deterministic and random design variables. The boundaries are constructed using a support vector machine that provides a way to efficiently evaluate probabilities of failure and solve the reliability-based design optimization problem. Another major advantage of the approach is that it efficiently manages the discontinuities that might appear during subcritical limit cycle oscillations. The proposed approach is applied to the construction of flutter and subcritical limit cycle oscillation boundaries for a two-degree-of-freedom airfoil with nonlinear stiffnesses. The solution of a reliability-based design optimization problem with a constraint on the probability of subcritical limit cycle oscillation is also provided. [ABSTRACT FROM AUTHOR]