In this talk, I will discuss several generalized versions, dependent on different boundary conditions, of the classical Gaffney-Friedrichs inequality for differential forms in Heisenberg groups. In the first part I will consider horizontal differential forms and the horizontal differential. In the second part, I will illustrate the counterpart of these results in the context of the Rumin’s complex. The results presented in this talk are obtained jointly with B. Franchi and E. Serra of the University of Bologna.