The total and the differential cross sections for the reaction e+e- --
> gammagamma(gamma) have been measured with the DELPHI detector at LEP
using an integrated luminosity of 36.9 pb-1. The results agree with t
he QED predictions and consequently there is no evidence for non-stand
ard channels with the same experimental signature. The lower limits ob
tained on the QED cutoff parameters are LAMBDA+ > 143 GeV and LAMBDA-
> 120 GeV, and the lower bound on the mass of an excited electron with
an effective coupling constant lambda(gamma) = 1 is 132 GeV/c2. Upper
limits on the branching ratios for the decays Z0 --> gammagamma, Z0 -
-> pi0gamma, Z0 --> etagamma and Z0 --> gammagammagamma have been dete
rmined to be 5.5 x 10(-5), 5.5 x 10(-5), 8.0 x 10(-5), and 1.7 x 10-5
respectively. All the limits are at the 95% confidence level.