The existing classification of evolutionarily singular strategies in Adaptive Dynamics assumes an invasion exponent that is differentiable twice as a function of both the resident and the invading trait. Motivated by nested models for studying the evolution of infectious diseases, we consider an extended framework in which the selection gradient exists (so the definition of evolutionary singularities extends verbatim), but where the invasion fitness may lack the smoothness necessary for the classification `a la Geritz et al. We derive the classification of singular strategies with respect to their convergence stability and invadability and determine the condition forthe existence of nearby dimorphisms. Contrary to the standard setting of Adaptive Dynamics, the fate of dimorphisms nearby a singular strategy can, in general, not be deduced from the monomorphic invasion exponent. We will present a formula that allows one to deduce the fate of dimorphisms from the dimorphic invasion exponent and demonstrate our findings on a specific example from evolutionary epidemiology.