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Double-tag events in two-photon collisions are studied using the L3 detector at LEP centre-of-mass energies from root(s)=189 GeV to 209 GeV. The cross sections of the e+e- -> e+e- hadrons and gamma*gamma* -> hadrons processes are measured as a function of the photon virtualities, Q1^2 and Q2^2, of the two-photon mass, W_gammagamma, and of the variable Y=ln(W_gammagamma^2/(Q1 Q2)), for an average photon virtuality <Q2> = 16 GeV2. The results are in agreement with next-to-leading order calculations for the process gamma*gamma* -> q qbar in the interval 2 <= Y <= 5. An excess is observed in the interval 5 < Y <= 7, corresponding to W_gammagamma greater than 40 GeV . This may be interpreted as a sign of resolved photon QCD processes or the onset of BFKL phenomena.