Double-tag events in two-photon collisions are studied using the L3 detector at LEP centre-of-mass energies from QY*Y* GeV to 209 GeV. The cross sections of the e+e−→e+e−hadrons and QY*Y* processes are measured as a function of the product of the photon virtualities, QY*Y*, of the two-photon mass, Wγγ, and of the variable Y=ln(W2γγ/Q2). The average photon virtuality is 〈Q21〉=〈Q22〉=16 GeV2. The results are in agreement with next-to-leading order calculations for the process √s=189 in the interval 2⩽Y⩽5. An excess is observed in the interval 5