Partial cross sections for the photoion formation from C(60) and C(70) were determined from the yields of singly, doubly, and triply charged ions which were measured by mass spectrometry combined with tunable synchrotron radiation at hnu = 25-120 eV. The dependence of the detection efficiencies on the mass-to-charge ratio was evaluated by using the formula proposed by Twerenbold et al. Corrections of the detection efficiency were found to be critical for obtaining accurate partial cross sections for photoionization of fullerenes. Revisions were made of the partial cross-section curves for single and double photoionization of C(60) and C(70). The curve for triple photoionization of C(70) was newly proposed. The ratios between the cross sections for double and single photoionization increase with hnu and reach saturated values of 0.78 at 85 eV for C(60) and approximately 1.3 at 100 eV for C(70). In contrast, the ratios at 120 eV between the cross sections for triple and single photoionization of C(60) and C(70) amount to 0.14 and approximately 0.38, respectively. The formation mechanism of multiply charged fullerene ions was discussed in terms of valence-electron excitation to antibonding unoccupied orbitals and/or spherical standing waves inside the cavity of a fullerene. This excitation could be followed by Spectator Auger processes and transmission of the excess electronic energy among numerous vibrational degrees of freedom.