The time-variant system reliability analysis is a challenging and significant topic, which also faces the common obstacles of traditional system reliability methods such as combination explosion and unclear correlation information. In this paper, the probability density evolution method (PDEM) for two types of time-variant system reliability analysis is proposed. First, the system reliability is classified into two types, and the corresponding equivalent performance functions are given, which are further extended to time-variant structural systems. Second, based on the single equivalent performance function, the generalized density evolution equation (GDEE) for time-variant structural system is derived in two different ways. Third, the GDEE is solved by the Dirac sequence method and the time-variant system reliability is evaluated. Finally, several numerical examples are investigated to illustrate the accuracy and effectiveness of proposed method. (C) 2017 American Society of Civil Engineers.