A primary concern in practical engineering design is ensuring high system reliability throughout a product life-cycle subject to time-variant operating conditions and component deterioration. Thus, the capability to deal with time-dependent probabilistic constraints in reliability-based design optimization is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. The NERS employs the stochastic process model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization technique is integrated with NERS to efficiently extract the extreme time response with respect to limit state function for a given system design. Third, an adaptive response prediction and model maturation mechanism is developed to facilitate the integration of NERS with iterative design process in RBDO. With the nested response surface of time, the time-dependent reliability analysis can be converted into the timeindependent reliability analysis and existing advanced reliability analysis and design methods can be used. The NERS is integrated with RBDO for the design of engineered systems with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of NERS approach.