  In this paper, we are interested in the construction of a bilinear
pseudodifferential calculus. We define some symbolic classes which contains
those of Coifman-Meyer. These new classes allow us to consider operators
closely related to the bilinear Hilbert transform. We give a description of the
action of our bilinear operators on Sobolev spaces. These classes also have a
``nice'' behavior through the transposition and the composition operations that
we will present.
