Let F be a totally real field and G=GSp(4)_{/F}. In this paper, we show under
a weak assumption that, given a Hecke eigensystem lambda which is
(p,P)-ordinary for a fixed parabolic P in G, there exists a several variable
p-adic family underline{lambda} of Hecke eigensystems (all of them (p,P)-nearly
ordinary) which contains lambda. The assumption is that lambda is cohomological
for a regular coefficient system. If F=Q, the number of variables is three.
Moreover, in this case, we construct the three variable p-adic family
rho_{underline{lambda}} of Galois representations associated to
underline{lambda}. Finally, under geometric assumptions (which would be
satisfied if one proved that the Galois representations in the family come from
Grothendieck motives), we show that rho_{underline{lambda}} is nearly ordinary
for the dual parabolic of P. This text is an updated version of our first
preprint (issued in the "Prepublication de l'universite Paris-Nord") and will
appear in the "Annales Scientifiques de l' E N S"
