In a sample of 19 x 10(6) produced B mesons, we have observed the decays B
--> eta K* and improved our previous measurements of B --> eta'K. The branc
hing fractions we measure for these decay modes are B(B+ --> eta K*(+)) = (
26.4(-8.2)(+9.6) +/- 3.3) X 10(-6), B(B-0 --> eta K*(0)) = (13.8(-4.6)(+5.5
) +/- 1.6) X 10(-6) B(B+ --> eta'K+) = (80(-9)(+10) +/- 7) X 10(-6), and B(
B-0 --> eta'K-0) = (89(-16)(+18) +/- 9) X 10(-6). We have searched with com
parable sensitivity for related decays and report upper limits for these br
anching fractions.