The regularized moment equations of rarefied gas dynamics provide stable sets of macroscopic equations to approximate to the Boltzmann equation [1,2].For monatomic gases,the regularized 13 moment system is required for third order accuracy in the Knudsen number (i.e.,super-Burnett order).We extend the idea to polyatomic gases using orders of magnitude in Knudsen numbers [3].The proposed model is based on a kinetic model equation of BGK-type,which is governed by two di erent Knudsen numbers,based on the mean free paths of particle collisions with and without exchange of internal degrees of freedom.We chose a set of 36 moment equations which we close by means of Grad’s distribution function for polyatomic gases.