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We calculate the leading order BFKL amplitude for the exclusive diffractive process \gamma*_L(Q1^2) \gamma*_L(Q2^2) \to \rho_L^0 \rho_L^0 in the forward direction, which can be studied in future high energy e^+e^- linear colliders. The resummation effects are very large compared to the fixed-order calculation. We also estimate the next-to-leading logarithmic corrections to the amplitude by using a specific resummation of higher order effects and find a substantial growth with energy, butdoi:10.1140/epjc/s10052-007-0375-7 fatcat:jngv2fzpfjcy3io5xsp5w33tci