  The hypothetic R--resonance production (anomalous "$l\bar l\gamma\gamma$"
events at LEP) with 60 GeV mass at FNAL hadron collider has been considered.
The cross-section of this R-resonance production with the consequent decay $R
\to \gamma\gamma$ is obtained. Various distributions of leptons and photons in
the process $p\bar p \to l\bar l R (\to \gamma\gamma) X$ are calculated.
