The intensity-dependent transmission of picosecond ruby laser pulses of different duration through methanolic and ethanolic solutions of rhodamine B and rhodamine 6G is analysed. The transmission is affected by S 0 -S" two-photon absorption, by stimulated emission at the pumplaser frequency, by amplified spontaneous emission and by excited-state absorption. Various parameters involving the two-photon absorption dynamics are determined by comparing experiments with numerical simulations.