Time delays in density dependence have been associated with regular and sustained fluctuations in population size. Mathematical models have found that delays that are long enough can produce limit cycles. In experimental populations with preadult and adult phases in the life cycle and density regulation in any of the phases, it has been found that the time delay represented by maturation time can produce fluctuations in adult size. This has been corroborated by mathematical models. The present study develops mathematical models of growth in this type of population. The analysis of these models indicate that when preadult cohorts do not overlap in space, and preadult mortality is affected by the density of preadults at the present moment, the time delay does not destabilize the population. However, with spatial overlap of preadult cohorts and the same mechanism of density dependence, time delays can be destabilizing. It is concluded that time delays in density effects during preadulthood are not necessarily destabilizing, and that fluctuations in population size can also be due to delays with density effects in preadulthood and adulthood, or exogenous agents. Copyright 1998 Academic Press Limited