Summary: As a continuation of Part I [Acta Math. Sin., Engl. Ser. 23, No. 2, 201–208 (2007; Zbl 1113.93103
)], this paper studies continuous time quasi-birth-and-death processes. Explicit necessary and sufficient conditions of
-ergodicity, geometric ergodicity for such quasi-birth-and-death processes are obtained and the authors prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.