中文摘要：

动力稳定性理论的研究属于基础理论问题，它的发展依赖于数学的发展，同样对它的研究也推动了数学的发展。至今为止，已经出现多种有关研究动力稳定性的数学方法，本文对动力稳定性研究中的典型的数学方法逐一进行了简单介绍，并对有关问题作出简要评述。

英文摘要：

The researches of dynamical stability theory belong to the basic problems in the scientific fields, and their developments and the progresses in math. depend on each other. So far, many mathematical methods on dynamical stability have been advanced. In this article, many kinds of typical method in math. on dynamical stability are introduced simply, furthermore, some related problems are commented briefly.