1. Cyclic dynamics of various periods are pervasive in many insect populations where interactions with natural enemies are known to be important. How stage-structured processes within the host population, such as competition and cannibalism, affect these interactions has received little attention so far. 2. Using the well- studied laboratory host-parasitoid system of Plodia interpunctella and Venturia canescens, we explore a series of host-parasitoid models of increasing complexity. Specifically, we identify the circumstances under which stage- structured processes both within the host and parasitoid populations generate dynamical behaviour ranging from generation to true consumer -resource (multi- generation) cycles. 3. We find that both within- host interactions (strong competition and egg cannibalism by late instar larvae) and parasitoid recruitment structure (a developmental lag in the parasitism of larvae) can suppress long period cycles and promote host generation cycles. In short, we show that simple stage- structured processes in both host and parasitoid can modulate the strength of the consumer -resource interaction. 4. For some parameters we find more than one stable cyclic attractor. The presence of multiple attractors means that the same mechanism can give rise to cycles of different periods depending on initial population numbers. Because the host- alone system may exhibit transient dynamics for a substantial period, the timing of a parasitoid invasion can be crucial to the dynamical outcome. 5. We discuss the consequences of using a single descriptor of an ecological time series, the cycle period, to infer properties about the underlying system and its food web interactions. Parasites diseases and disorders; Parasites; Insect parasites; Hosts; Insect hosts; Ecology Plodia interpunctella (Pyralidae); Hymenopteran parasites; Venturia canescens; Host parasite cyclic population dynamics related to stage structured processes; Population dynamics Venturia canescens (Ichneumonidae); Lepidopteran hosts; Plodia interpunctella; Host parasite cyclic population dynamics related to stage structured processes; Population dynamics none