A functional equation arising firom kinetic theory of dense gases is considered. The solutions to this equation represent the quillbrium distniutions for the revised Enskog Equation. Indeed, they make the Rdsiiois-Polewczak Liapounov fUncti0∼1 constant m time. The class of all the above mentioned distriiutions is completely characterized. This class is wider than that characterized by Risibois only consisting of the distributions which are periodic with respect to the space variable.