The production of photon pairs in e+e- --> ffgammagammaBAR processes i
s studied using exact helicity amplitudes at tree level. Total cross s
ections, including initial state radiation effects, are given. They ar
e presented in the case of quarks as a function of y(cut) in the JADE
algorithm. In the case of leptons we use cuts similar to the ones empl
oyed in a recent L3 analysis. Masses of the final state fermions are t
aken into account when appropriate. The cross section e+e- --> tau+tau
-gammagamma is about 10% larger when the tau mass is neglected. We obt
ain, with a different method, results which are in good agreement with
L3 Monte Carlo simulation.