  In this paper we provide a characterization of second order fully nonlinear
CR invariant equations on the Heisenberg group, which is the analogue in the CR
setting of the result proved in the Euclidean setting by A. Li and the first
author (2003). We also prove a comparison principle for solutions of second
order fully nonlinear CR invariant equations defined on bounded domains of the
Heisenberg group and a comparison principle for solutions of a family of second
order fully nonlinear equations on a punctured ball.
