The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator–prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a ‘phase space core’ of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar systems. Finally, we show how the presence of semistable equilibria increases the number of possible Allee effect cores.