  Using 58 million $J/\psi$ events collected with the Beijing Spectrometer
(BESII) at the Beijing Electron-Positron Collider, the decays $J/\psi\to
\gamma\phi\rho$ and $J/\psi\to \gamma\omega\rho$ are searched for, and upper
limits on their branching fractions are reported at the 90% C. L. No clear
structures are observed in the $\gamma \rho$, $\gamma \phi$, or $\rho \phi $
mass spectra for $J/\psi\to \gamma\phi\rho$ nor in the $\gamma \rho$, $\gamma
\omega$, or $\rho \omega$ mass spectra for $J/\psi\to \gamma\omega\rho$.
