  We present a search for decays of $B$ mesons to final states with a $b\_1$
meson and a $\rho$ or $K^*(892)$ meson. The search is based on a data sample
consisting of 465 million $B\kern 0.18em{\kern -0.18em B}{}$ pairs collected by
the {\slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller
A\kern-0.2em R}} detector at the SLAC National Accelerator Laboratory. We do
not observe any statistically significant signal. The upper limits we set on
the branching fractions range from 1.4 to $8.0 \times 10^{-6}$ at the 90%
confidence level (C.L.), including systematic uncertainties.
