  The BGK model is a relaxation-time approximation of the celebrated Boltzmann
equation, and the Marle model is a direct extension of the BGK model in a
relativistic framework. In this paper, we introduce the Marle model for
polyatomic gases based on the J\"{u}ttner distribution devised in [Ann. Phys.,
377, (2017), 414--445], and show the existence of a unique set of equilibrium
parameters of the J\"{u}ttner distribution.
