Near-Earth Asteroids (10302) 1989 ML and (4660) Nereus have attracted much attention as candidates for deep space explorations of the next generation. In the study, the maximum Lyapunov exponent (MLE) and MEGNO index (Mean Exponential Growth factor of Nearby Orbits) are calculated after considering the effects of major objects of the Solar system and the stability of these two asteroids are discussed. For each asteroid, 1000 clonal particles are generated from a multivariate normal distribution within the observational uncertainties. The statistical results display probable motion regions of each asteroid within 0.1 million years, and provide distributions of occurrence times in the phase space of semi-major axis versus eccentricity, and count probability of close encounters and collisions between asteroid and Earth or other planets. Further, secular resonance, Kozai resonance and mean motion resonance are analyzed for nominal orbits of the two asteroids. By these analyses above, we concluded that 1989 ML is in the region dominated by mean motion resonances with terrestrial planets, and the probability of close encounters with them is relatively small. Therefore, its orbit is relatively stable. For Nereus, it is located in the close-encounter region of the Earth with an extremely unstable orbit.