  In a sample of 19 million produced B mesons, we have observed the decays B ->
eta K* and improved our previous measurements of B -> eta'K. The branching
fractions we measure for these decay modes are BR(B+ -> eta K*+) = (26.4
+9.6-8.2 +- 3.3) x $10^{-6}$, BR(B0 -> eta K*0) = (13.8 +5.5-4.6 +- 1.6) x
$10^{-6}$, BR(B+ -> eta' K+) = (80 +10-9 +- 7) x $10^{-6}$ and BR(B0 -> eta'
K0) = (89 +18-16 +- 9) x $10^{-6}$. We have searched with comparable
sensitivity for related decays and report upper limits for these branching
fractions.
