Most models of population dynamics do not take sexual reproduction into account (i.e. they do not consider the role of males). However, assumptions behind this practice—that no demographic sex differences exist and males are always abundant enough to fertilize all the females—are usually not justified in natural populations. On the contrary, demographic sex differences are common, especially in polygynous species. Previous models that consider sexual reproduction report a stabilizing effect through mixing of different genotypes, thus suggesting a decrease in the propensity for complex dynamics in sexually reproducing populations. Here we show that considering the direct role of males in reproduction and density dependence leads to the conclusion that a two–sex model is not necessarily more stable compared with the corresponding one–sex model. Although solutions exist where sexual reproduction has a stabilizing effect even when no genotypic variability is included (primarily when associated with monogamy), factors like polygyny, sex differences in survival or density dependence, and possible alterations of the primary sex ratio (the Trivers–Willard mechanism), may enlarge the parametric region of complex dynamics. Sexual reproduction therefore does not necessarily increase the stability of population dynamics and can have destabilizing effects, at least in species with complicated mating systems and sexual dimorphism.