In this paper, we consider the direct application of the relativistic extended thermodynamics theory of polyatomic gases developed in Ann. Phys. 377 (2017) 414--445 to the relativistic BGK model proposed by Marle. We present the perturbed Marle model around the generalized J\"uttner distribution and investigate the properties of the linear operator. Then we prove the global existence and large-time behavior of classical solutions when the initial data is sufficiently close to a global equilibrium.
Byung-Hoon Hwang (Sun,) studied this question.