Abstract We discuss the dynamics of asteroids possessing perihelion distances shorter than 0.15 au because this value is close to the perihelion distance of (3200) Phaethon (0.14 au). A well-elaborated force model is necessary to describe the motion of the discussed objects. In this study, we examined the following factors affecting an asteroid's motion: perturbations from all major planets and those from Pluto, Moon, Ceres, Pallas, and Vesta, Sun's and Jupiter's oblateness, relativistic effects of the Sun and all major planets (as well as Pluto and the Moon), solar radiation pressure, and the Yarkovsky effect. All five methods are based on the analysis of (O–C) residuals (differences between the observed and calculated coordinate values), the size of the initial confidence region, and the orbital evolution. This demonstrates that there exists a close correlation between all five methods. We arranged the perturbing forces in accordance with their power as follows (the most powerful first): perturbations from major planets, from the Moon, the relativistic effects of the Sun, and the Sun's oblateness. The relativistic effects of the other bodies were negligible. In addition, we paid special attention to the Yarkovsky effect. Our results showed that it significantly affected the asteroid motion. However, currently, we cannot confidently and precisely isolate its contribution to the full force model because of the insufficient precision of its parameter definition. The obtained results could be used to study the dynamics of near-Sun asteroids, which we illustrate by exploring the orbital evolution of the (3200) Phaethon asteroid.