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In this paper, we consider spatially flat FLRW cosmological models in twocontexts in an attempt to derive a set of conditions that characterize whensuch models exhibit oscillatory behaviour. In the first case, we consider aspatially flat FLRW model with only a minimally-coupled scalar field, describedby a nonnegative scalar field potential. In the second case, we extended thismodel to include barotropic matter. We show that for the case of a positivecosmological constant, spatial flatness, and barotropic matter, oscillatorysolutions are certainly possible. However, these solutions do not oscillateindefinitely, they decay over time. Interestingly, it is shown that all suchsolutions oscillate and decay towards the de Sitter equilibrium point, whichrepresents an inflationary epoch in such models. This implies that for certainfamilies of scalar field potentials, the universe may have undergone severaloscillations \emph{before} entering an inflationary epoch.

Oscillating Towards the de Sitter Universe