The dynamical consequences of multiple-species interactions remain an elusive and fiercely debated topic. Recently, Murdoch and colleagues proposed a general rule for the dynamics of generalist natural enemies: when periodic, they exhibit single generation cycles (SGCs), similar to single species systems. This contrasts markedly with specialists, which tend to show classic (longer period) consumer-resource cycles. Using a well-studied laboratory system, we show that this general rule is contradicted when we consider resource age-structure. Parasites diseases and disorders; Parasites; Insect parasites; Hosts; Insect hosts; Ecology Ephestia kuehniella; Plodia interpunctella (Pyralidae ); Hymenopteran parasites; Venturia canescens; Natural enemy specialization & period of population cycles, models Venturia canescens (Ichneumonidae); Lepidopteran hosts; Ephestia & Plodia; Natural enemy specialization & period of population cycles, models; Population dynamics; Population cycles none