We investigate quantitatively the effects of strong electron - electron coupling on the dynamics of lattice electrons. For this purpose the self-consistent version of the bubble-chain approximation at zero temperature and half filling of the Anderson (Hubbard) model is used. Special attention is paid to a critical region of an electron - hole correlation function shaping the transition from weak to strong interaction. We find an analytic solution with Fermi-liquid properties on the weak-coupling side of the critical region around the two-particle pole. It is shown that Fermi-liquid theory does not lead to a consistent behaviour of the self-consistent solution on the strong-coupling side of the critical region.