The Near-Earth Asteroids (NEAs) are dynamically classified according to their orbital characteristics into four groups: Atens, Apollo, Amor and Atira. The orbital evolution of the NEAs is dominated by the gravitational interaction with the terrestrial planets in such way that a single close encounter with one of these planets can move the asteroid from one group to another. The goal of this work was to study the temporal orbital evolution of the NEAs paying special attention to their mobility as a function of their initial location in the semi-major axis versus eccentricity plane (a x e), and consequently in their transition between the groups. Our method was based on numerical integrations of the gravitational N-body problem. We analyzed the temporal evolution of the orbit of each NEA. Our simulations showed cases where a single asteroid experienced four change of group. In other cases, some NEAs spend their whole life oscillating between only two groups, and we also found some NEAs that do not experience a change in the initial group that they belonged to. We then characterized the transition of these asteroids among the groups along their lifetime within the population of NEAs, and we analyzed how this is related to the initial orbit of the asteroid in terms of their initial semi-major axis, eccentricity and inclination. The results of this analysis suggest that in fact, the usual classification of NEAs between groups in a statical approach is actually a “snapshot” of the population. Nevertheless, we were able to find some patterns, which allow us to propose a new dynamical classification to the NEAs.