  The decay rates of $c\bar{c}$ and $b\bar{b}$ through two-photon or two-gluon
annihilations are obtained by using totally relativistic decay amplitudes and a
sophisticated quantum-chromodynamic potential model for heavy quarkonia. Our
results for the photonic and gluonic widths of the 1S0, 3P0, and the 3P2 states
are in excellent agreement with the available experimental data. The procedures
and mathematical techniques used by us for the treatment of the
fermion-antifermion bound states are also applicable to other decay processes.
