  We calculate the cross-section for the diffractive exclusive process gamma*_L
(Q_1^2) gamma*_L(Q_2^2) -> rho^0_L rho^0_L, in view of its study in the future
high energy e+e- linear collider. The Born order approximation of the amplitude
is completely calculable in the hard region Q_1, Q_2 >> Lambda_QCD. The
resulting cross-section is large enough for this process to be measurable with
foreseen luminosity and energy, for Q_1 and Q_2 in the range of a few GeV.
