We investigate some implications of having two star formation episodes in globular clusters, rather than the traditional single-burst approximation. Evidence for more than one stellar generation is accumulating in observations of abundances of elements lighter than iron in globular cluster stars, and is thought to imply some self-enrichment of the globular cluster gas. In particular, we explore models based on the assumption that the self-enrichment comes from an early generation of asymptotic giant branch (AGB) stars.