Double-tag events in two-photon collisions are studied using the L3 detector at LEP centre-of-mass energies from √s = 189 GeV to 209 GeV. The cross sections of the e+e− → e+e−hadrons and γ ∗γ ∗ → hadrons processes are measured as a function of the product of the photon virtualities, Q2 = Q2 1Q2 2, of the two-photon mass, Wγ γ , and of the variable Y = ln(W2 γ γ /Q2). The average photon virtuality is Q2 1=Q2 2 = 16 GeV2. The results are in agreement with next-to-leading order calculations for the process γ ∗γ ∗ → qq in the interval 2 ̄ Y 5. An excess is observed in the interval 5 < Y 7, corresponding to Wγ γ greater than 40 GeV. This may be interpreted as a contribution of resolved photon QCD processes or the onset of BFKL phenomena.