  The B --> rho0 rho0 decay mode is searched for in a data sample of about 227
million Upsilon(4S) --> B Bbar decays collected with the BABAR detector at the
PEP-II asymmetric B factory at SLAC. No significant signal is observed, and an
upper limit of 1.1 x 10e-6 (90% C.L.) on the branching fraction is set.
Implications on the penguin contribution and constraints on the CKM angle alpha
with B --> rho rho decays are discussed. All results are preliminary.
