Absolute values of the two-photon absorption cross-sections of Rhodamine 6G, Rhodamine B, Acridine Red, Disodium Fluorescein and DODCI have been obtained by excitation with a neodymium:glass laser (1060 nm). Measurements over eight orders of magnitude of the exciting light flux were carried out by employing the laser both Q-switched and mode-locked. The two-photon fluorescence flux measurements were calibrated by single-photon fluorescence generated by excitation with second-harmonic laser pulses. The experimental results are compared with values predicted by semi-empirical theoretical models and good agreement is obtained. Two-photon amplification of the mode-locked neodymium laser by organic dyes is shown not to be practicable at present. Other possible two-photon oscillators are discussed.