It has been proposed that carbon nitride compounds could present abnormal mechanical properties. Until now, these compounds have only been synthesized as amorphous films and the search for their structure is a live topic. Using ab-initio calculations, we propose a few stable structures which could be in dynamical equilibrium. We suggest that CNx (x = 0.33) structural arrangements dynamically equilibrate over the time which is necessary to perform a structural measurement and that mote than one structure could be needed to describe them.