  Polarized and $G$-polarized CR manifolds are smooth manifolds endowed with a
double structure: a real foliation $\Cal F$ (given by the action of a Lie group
$G$ in the $G$-polarized case) and a transverse CR distribution $(E,J)$.
Polarized means that $(E,J)$ is roughly speaking invariant by $\Cal F$. Both
structures are therefore linked up. The interplay between them gives to
polarized CR-manifolds a very rich geometry.
  In this paper, we study the properties of polarized and $G$-polarized
manifolds, putting special emphasis on their deformations.
