Molecular oxygen was selectively excited to several vibrational levels of the A 3-SIGMA-u+, A'3-DELTA-u and c 1-SIGMA-u- states by absorption of pulsed dye-laser emission. Time-resolved fluorescence could be observed in the O2(b 1-SIGMA-g+ --> X 2-SIGMA-g-) band at lambda = 762 nm. From the temporal behaviour of this emission, a lower limit of the rate constant for quenching of O2(A 3-SIGMA-u+) by oxygen itself could be deduced to be greater-than-or-equal-to 1 x 10(-11) cm3 s-1 for the vibrational levels upsilon' = 7, 8. The data for the intensity of the O2(b 1-SIGMA-g+ --> X 3-SIGMA-g-) emission as a function of the O2/N2 mixing ratio suggest that not all the quenching of the ungerade states leads to population of the O2(b 1-SIGMA-g+) state.