The variety of models that are currently being used in predictive microbiology or microbial ecology aiming at reproducing the growth curve of microorganisms were reviewed leading to focus on the only two models that are shown to capture qualitative features that appear in experiments. These models capture naturally the lag phase, that is, Baranyi and Roberts model and the neoclassical model were analyzed. In both models, the lag is associated with unstable stationary points and linked to the general behavior of solutions having initial conditions in the neighboorhood of unstable stationary points. This general behavior consists of the solution departing very slowly away from this neighboorhood. A meaningful interpretation to the 'physiological state of the cells at inoculation' a parameter introduced by Baranyi and Roberts that has a profound impact on microbial growth was provided in terms of the initial cell concentration and the initial growth rate, but is shown to be independent of 'the history of the cells'. A new, more natural, and biologically meaningful formulation of lag duration is proposed in terms of the initial conditions being in the neighbourhood of one of the unstable stationary points revealed by both models.

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