The life cycle of many endoparasites can be delayed by free-living infective stages and a developmental arrestment in the host referred to as hypobiosis. We investigated the effects of hypobiosis and its interaction with delay in the free-living stages on host-parasite population dynamics by expanding a previous attempt by Dobson & Hudson. When the parasite life cycle does not include free-living stages, hypobiosis destabilizes the host-parasite interactions, irrespective of the assumptions about the regulation of the host population dynamics. Interestingly, the destabilizing effect varies in a nonlinear way with the duration of hypobiosis, the maximal effect being expected for three to five months delay. When the parasite life cycle involves free-living stages, hypobiosis of short or intermediate duration increases the destabilizing effect of the first time delay. However, hypobiosis of a duration of five months or more can stabilize interactions, irrespective of the regulation of the host population dynamics. Overall, we confirmed that hypobiosis is an unusual time delay as it can stabilize a two-way interaction. Contrary to the previous conclusions, such an atypical effect does not require self-regulation of the host population, but instead depends on the existence of free-living stages.