  New measurements are presented of the photon structure function F_2^gamma(Q)
at four values of Q^2 between 9 and 59 GeV/c^2 based on data collected with the
OPAL detector at centre-of-mass energies of 161-172 GeV, with a total
integrated luminosity of 18.1 pb^-1. The evolution of F_2^gamma with Q^2 in
bins of x is determined in the Q^2 range from 1.86 to 135 GeV/c^2 using data
taken at centre-of-mass energies of 91 GeV and 161-172 GeV. F_2^gamma is
observed to increase with Q^2 with a slope of 1/alpha_em dF_2^gamma/dln(Q^2) =
0.10 +0.05 -0.03 measured in the range 0.1 < x < 0.6.
