We have searched for new light gauge bosons produced in pi0 and eta de
cays by studying the kinematically well-constrained reactions ppBAR --
> pi0pi0pi0 and ppBAR --> pi0pi0eta, where one pi0 or the eta decays t
hrough the emission of a single photon recoiling against a missing sta
te X (where X is a long-lived weakly interacting particle or X --> nun
uBAR). No signal has been observed and branching ratio upper limits of
6 x 10(-5) at 90 % C.L. have been obtained for masses of the gauge bo
son lying between approximately 65 MeV and 125 MeV (pi0 decay), and 6
x 10(-5) at 90 % C.L., for X masses between approximately 200 MeV and
525 MeV (eta decay). The pi0-decay limit represents a factor of 4 to 8
improvement when compared to the existing limit, whereas the eta deca
y limit has been measured for the first time, thereby extending the m(
X) range from 130 MeV up to 525 MeV.