  We derive bounds on Higgs and gauge--boson anomalous interactions using the
CDF data for the process $p \bar{p} \to \gamma\gamma\gamma + X$. We use a
linearly realized $SU_L(2) \times U_Y(1)$ invariant effective Lagrangian to
describe the bosonic sector of the Standard Model, keeping the fermionic
couplings unchanged. All dimension--six operators that lead to anomalous Higgs
interactions involving $\gamma$ and $Z$ are considered. We also show the
sensitivity that can be achieved for these couplings at Fermilab Tevatron
upgrades.
