We have calculated nonlinear time correlation functions of a dilute hard-sphere gas numerically by using the Monte Carlo method, to find that the single particle dynamics in a dilute hard-sphere gas does not follow the Gaussian process. The deviation of the self-part of the dynamic structure factor from a Gaussian function is observed. This non-Gaussian character corresponds to those of Lennard-Jones liquids reported by Itagaki [K. Itagaki, M. Goda, and H. Yamada, Physica A 265, 97 (1999)], if we scale the time unit by the collision frequency. Further, we trapped a particle in a harmonic well and calculated the time development of its distribution, in order to clarify the effect of collisions to the solvation dynamics. Both the Gaussian and the linear response assumptions are broken, and the deviation becomes larger as the curvature of the harmonic well gets larger. (C) 2001 American Institute of Physics.