We address the problem of passive modelocking in class-B lasers with saturable abosrber taking into account the fast dynamics of both gain and absorption. Our model, which is derived from a delay differential equation model, treats in a rigorous way the definition of the fast and slow times which are typically used in the master equation approach. In that way all the dynamical variables obey exact periodic boundary conditions and this makes the model suitable for analytic and numerical

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... . The model accounts for behaviours different from fundamental modelocking, such as Q-switching modelocking and harmonic modelocking.