The reliability-based optimization of uncertain linear structural systems subjected to stochastic excitation is considered. Uncertain system parameters are modeled as random variables with prescribed joint probability density function. Second-order probabilistic descriptors are combined with approximate extreme response theories to obtain conditional reliability estimates for the system. Approximations based on asymptotic expansions are used to provide a computationally efficient estimate for the unconditional system reliability that accounts for the uncertainties in the system parameters. A general solution strategy for the corresponding reliability-based optimization problem is presented. Implementation issues related to the evaluation of system response functions and calculation of design points are addressed. The effects of uncertainty in the system parameters, as well as the accuracy of reliability estimates on the optimal design, are investigated. It is shown that these two factors are important because they can change the optimal design significantly. A generic primary-secondary system is presented to illustrate the performance and efficiency of the proposed implementation.