A classification of spiking neurons according to the transition from quiescence to periodic firing of action potentials is commonly used. Nonbursting neurons are classified into two types, type I and type II excitability. We use simple phenomenological spiking neuron models to derive a criterion for the determination of the neural excitability based on the after potential following a spike. The crucial characteristic is the existence for type II model of a positive overshoot, that is, a delayed after depolarization, during the recovery process of the membrane potential. Our prediction is numerically tested using well-known type I and type II models including the Connor, Walter, & McKown (1977) model and the Hodgkin-Huxley (1952) model.