Exclusive rho rho production in two-photon collisions between a quasi-real, gamma, and a virtual, gamma*, photons is studied at LEP at centre-of-mass energies 89 GeV < sqrt{s} < 209 GeV with a total integrated luminosity of 854.7 pb-1. The cross sections of the gamma gamma* -> rho rho processes are determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, Wgg, in the kinematic region: 0.2 GeV^2 < Q^2 < 30 GeV^2 and 1.1 GeV < Wgg < 3 GeV.
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