  Exclusive rho+rho- production in two-photon collisions between a quasi-real
photon, gamma, and a mid-virtuality photon, gamma*, is studied with data
collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total
integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* ->
rho+ rho- process is determined as a function of the photon virtuality, Q^2,
and the two-photon centre-of-mass energy, W_gg, in the kinematic region:
0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together
with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a
study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2
< 30 GeV^2.
