The absorption cross section of highly luminescent individual single-walled carbon nanotubes is determined using time-resolved and cw luminescence spectroscopy. A mean value of approximately 1 x 10(-17) cm2 per carbon atom is obtained for (6,5) tubes excited at their second optical transition, and corroborated by single tube photothermal absorption measurements. Biexponential luminescence decays are systematically observed, with short and long lifetimes around 45 and 250 ps. This behavior is attributed to the band edge exciton fine structure with a dark level lying a few meV below a bright one.