We have investigated the dynamical evolution of asteroid (433) Eros, soon to be explored by the Near-Earth Asteroid Rendezvous (NEAR) probe, by performing 16 numerical integrations of "dynamical clones" of Eros's chaotic orbit over a timespan of 5 Myr. By analyzing the results of these integrations we have found the following: (1) In six cases a clone becomes an Earth crosser, typically because of eccentricity increases caused by the ν3 and ν4 secular resonances; two clones become Venus crossers, and one eventually collides with the Sun. (2) Some of the Earth-crossing clones go back to the Mars-crossing state after some time, and several have their inclination affected by the ν13 and ν14 nodal resonances. (3) Nine clones have a slow evolution dominated by Mars encounters, and one of them is temporarily trapped into the 25:24 mean motion resonance with Mars, providing effective protection from close encounters over more than 1 Myr. (4) From the number of planetary encounters recorded during our integrations, Eros's lifetime versus a collision with Earth and Mars can be estimated to be about 1.84 and 2.9 Gyr, respectively. (5) On the other hand, it is impossible to estimate even as an order of magnitude the past or future mean impact rate onto Eros's surface. These findings have the following implications: Eros's dynamical lifetime is probably of the order of 50–100 Myr, and it has ≈5% probability of eventually hitting Earth. Its shape may have been affected by tidal forces during past Earth encounters. Its birth location in the main belt cannot be traced back with certainty, but if Eros comes from a family-forming catastrophic breakup near one of the main resonances, this must have been one of the last such events to occur in the main belt. More likely, Eros's orbit became Mars crossing by slowly diffusing from the high-eccentricity portion of the main be then, Mars and Earth encounters led it to its current state. Unfortunately, the forthcoming observations of Eros's cratering record by the NEAR probe will not be useful to constrain its age or collisional lifetime.
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