A search for rare charmless decays of B-d(0) and B-s(0) mesons has bee
n performed in the exclusive channels B-d(s)(0)-->eta eta, B-d(s)(0)--
>eta pi(0) and B-d(s)(0)-->pi(0) pi(0). The data sample consisted of t
hree million hadronic Z decays collected by the L3 experiment at LEP f
rom 1991 through 1994. No candidate event has been observed and the fo
llowing upper limits at 90% confidence level on the branching ratios h
ave been set: Br(B-d(0)--eta eta) < 4.1 x 10(-4), Br(B-s(0)-->eta eta)
< 1.5 x 10(-3), Br(B-d(0)-->eta pi(0)) < 2.5 x 10(-4), Br(B-s(0)-->et
a pi(0)) < 1.0 x 10(-3), Br(B-d(0)-->pi(0) pi(0)) < 6.0 x 10(-5), Br(B
-s(0)-->pi(0) pi(0)) < 2.1 x 10(-4). These are the first experimental
limits on B-d(0)-->eta eta and on the B-s(0) neutral charmless modes.