本文围绕天体力学中的四体系统的层级稳定性展开。层级稳定是指：四体系统中的天体所在层级不变，且同一层级的天体轨道内外顺序不变。 研究四体系统的层级稳定性，旨在回答三个方面的问题：太阳系的现有层级结构是否稳定；近地小行星是否稳定以及如何捕获；主带小行星为何在火星和木星轨道之间呈环状分布。 四体系统可以根据是否有质量忽略不计的天体分为非限制性四体问题和限制性四体问题。本文首先研究了三类非限制性四体系统的稳定性，分别是行星层级四体系统、共面1-2-1型四体系统和共面1-3型四体系统。基于Sudman不等式，分别得到了系统稳定的解析准则，并将其应用于判定太阳系与系外星系中四体系统的稳定性。 其次讨论了两类限制性四体系统的稳定性，分别是双椭圆限制性四体系统和行星层级限制性四体系统。 从小天体的动力学方程出发，推导出小天体运动所满足的积分不变关系，从而得到了小天体的零速度曲面方程。之后从能量的角度建立四体系统的稳定性准则，结合数值方法讨论了近地小行星的捕获问题。 数值方法除了可以验证解析准则的正确性之外，还可以用来研究解析方法暂时无法回答的问题。例如“太阳-火星-木星-小行星”四体模型下主带小行星呈环状分布的问题。在研究过程中，提出了一种选择数值积分时长的方法。仿真数据利用概率神经网络来学习、训练，进而达到判定小行星稳定性的目的。在数值研究过程中，发现与大天体共振小行星的轨道偏心率变化较大。初始判定稳定的小行星可能由于偏心率增大而破坏稳定性。通过对小天体附加能量项的展开，找到了共振的影响机理。轨道共振时共振角长周期变化使得附加能量大幅度变化，进而改变小天体的总能量，影响小天体的层级稳定性。

This paper focuses on the hierarchical stability of the four-body system in celestial mechanics.Hierarchical stability means that all the bodies in the four-body system will not change their hierarchy, and the bodies in the same hierarchy will not exchange their orbits.The purpose of studying the hierarchical stability of the four-body system is to answer three questions: whether the existing hierarchical structure of the solar system is stable; whether the near-Earth asteroids are stable and how to capture them; why the main-belt asteroids are distributed in a ring between the orbits of Mars and Jupiter.According to whether there are massless bodies, the four-body system can be divided into the general four-body problem and restricted four-body problem.Firstly, the stability of three kinds of general four-body systems is studied. They are planetary four-body system, coplanar 1-2-1 configuration four-body system and coplanar 1-3 configuration four-body system. Based on the Sundman inequality, the analytical criteria of stability are obtained and applied to the four-body systems in the Solar and extrasolar systems.Secondly, the stability of two kinds of restricted four-body systems is discussed. They are elliptical restricted four-body system and planetary restricted four-body system. Based on the particle's dynamic equation, the integral invariant relation is deduced, and the zero-velocity surface of the particle is obtained. Then, the stability criteria of two kinds of restricted four-body systems are established from the point of view of energy. Combined with the numerical method, the capture of near-Earth Asteroids is discussed.In addition to verifying the analytical criteria, the numerical method can also be used to study the problems that cannot be solved analytically, such as the hierarchical stability of the `Sun-Mars-Jupiter-asteroid' four-body system. The main-belt asteroids are distributed in a ring between the orbits of Mars and Jupiter. A method to choose the numerical integration timescale is proposed. The simulation data are used to train the probabilistic neural networks. The trained neural networks can predict the stability of asteroids.It is found that the eccentricity of a particle could change greatly if it is resonant with a planet. These particles may be stable at initial but break the hierarchy due to the increase of eccentricity. By expanding the expression of the additional energy, the mechanism is found. Resonance makes the additional energy change greatly and then changes the particle's total energy, breaking the stability criteria.