  The structure of both quasi-real and highly virtual photons is investigated
using the reaction e+e- -> e+e-mu+mu-, proceeding via the exchange of two
photons.
  The results are based on the complete OPAL dataset taken at e+e-
centre-of-mass energies close to the mass of the Z boson.
  The QED structure function F_2^gamma and the differential cross-section
dsigdx for quasi-real photons are obtained as functions of the fractional
momentum x from the muon momentum which is carried by the struck muon in the
quasi-real photon for values of Q**2 ranging from 1.5 to 400 GeV**2.
  The differential cross-section dsigdx for highly virtual photons is measured
for 1.5< Q**2 < 30 GeV**2 and 1.5< P**2 < 20 GeV**2, where Q**2 and P**2 are
the negative values of the four-momentum squared of the two photons such that
Q**2 > P**2.
  Based on azimuthal correlations the QED structure functions F_A^gamma and
F_B^gamma for quasi-real photons are determined for an average Q**2 of 5.4
GeV**2.
