Abstract: Modern mechanical systems tend to adopt light flexiblematerials, and thus involve state variables with different time scales. Taking theunavoidable delay in control path into consideration, such kind of systemscan be modeled as slow-fast system with time delay. In this paper, somebasic facts of slow-fast systems are given firstly. Then, advances in thenonlinear dynamics of slow-fast systems with time delay are presented. Andfinally, several problems for future investigation are suggested.