  We search for the decays B0->rho0rho0, B0->rho0f0, and B0->f0f0 in a sample
of about 384 million Upsilon(4S)->BBbar decays collected with the BABAR
detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We find
evidence for B0->rho0rho0 with 3.5 sigma significance and measure the branching
fraction BR = (1.07+-0.33+-0.19)10^-6 and longitudinal polarization fraction
f_L = 0.87+-0.13+-0.04, where the first uncertainty is statistical, and the
second is systematic. The uncertainty on the CKM unitarity angle alpha due to
penguin contributions in B-> rho rho decays is 18 degrees at the 1 sigma level.
We also set upper limits on the B0->rho0f0 and B0->f0f0 decay rates.
