Virtual Compton scattering (VCS) on the proton has been studied at the Jefferson Laboratory using the exclusive photon electroproduction reaction ep -\u3e ep gamma. This paper gives a detailed account of the analysis which has led to the determination of the structure functions P-LL - P-TT/epsilon and P-LT and the electric and magnetic generalized polarizabilities (GPs) alpha(E) (Q(2)) and beta(M) (Q(2)) at values of the four-momentum transfer squared Q(2) = 0.92 and 1.76 GeV2. These data, together with the results of VCS experiments at lower momenta, help building a coherent picture of the electric and magnetic GPs of the proton over the full measured Q(2) range and point to their nontrivial behavior
