本文首先对单生过程、单死过程这两类极其重要的Markov 过程以及它们的特例生灭过程的经典问题（唯一性、常返性及遍历性）研究结论做了一个简要的归纳介绍. 然后对单生过程、单死过程进行推广得到双生双灭过程, 给出其常返性的显式判别准则. 并进一步给出双灭过程及双生过程常返性的显式判别准则.
作为应用, 在文末讨论了三个双生双灭过程的例子的常返性.

In this paper, a brief summary of the classical problems including uniqueness, recurrence, ergodicity of the single birth processes, the single death processes and the birth death processes is presented firstly. Then, the single birth processes are generalized to the double birth and double death processes. And the explicit criterion for recurrence of the double birth and double death processes is obtained. Furthermore, the explicit criteria for recurrence of the double birth processes and the double death processes are also founded.
As an application, the recurrence of some examples is illustrated at the end.