Estimates of the influence of the solar radiation pressure and the Yarkovsky effect on the long-term orbital dynamics are obtained for a number of asteroids experiencing successive approaches to planets. Based on the estimates of the change in the value of the asteroid’s proper rotation period obtained in (Melnikov, 2022) due to its approaches to the planets, the influence of such events on the further orbital dynamics of an asteroid through the Yarkovsky effect is considered. It is shown that close encounters with the planets of small asteroids (tens of meters in diameter) with fast rotation (proper rotation period less than 10 h), leading to a change in the asteroid rotation period by several hours, can change the magnitude of the Yarkovsky effect by 30–50%.