A study is made of the stability of triangular libration points in the nearly-circular restricted three-body problem in the spatial case. The problem of stability for most (in the sense of Lebesgue measure) initial conditions in the planar case has been investigated earlier. In the spatial case, an identical resonance takes place: for all values of the parameters of the problem the period of Keplerian motion of the two main attracting bodies is equal to the period of small linear oscillations of the third body of negligible mass along the axis perpendicular to the plane of the orbit of the main bodies. In this paper it is assumed that there are no resonances of the planar problem through order six. Using classical perturbation theory, KAM theory and algorithms of computer calculations, stability is proved for most initial conditions and the Nekhoroshev estimate of the time of stability is given for trajectories starting in an addition to the above-mentioned set of most initial conditions.

研究了空间情形下近圆受限三体问题中三角形振动点的稳定性。早先已经研究了平面情况下大多数（在勒贝格测度意义上）初始条件的稳定性问题。在空间情况下，发生相同的共振：对于问题的所有参数值，两个主要吸引体的开普勒运动周期等于第三个质量可忽略不计物体沿轴的小线性振荡周期垂直于主体的轨道平面。在本文中，假设通过六阶平面问题没有共振。利用经典微扰理论、KAM理论和计算机计算算法，