Transition strengths have been measured for the weak 2330Å band in XeF2 (f= 0.002) and for the two weak bands in XeF4 at 2280Å (f= 0.009) and 2580Å (f= 0.003). To investigate the origins of these weak transitions, the possibilities of vibronic and singlet-triplet transitions in XeF2 and XeF4 were examined. Using the Herzberg-Teller theory of vibronic transitions and a molecular orbital treatment of excited electronic states, estimated strengths of the relevant vibronic transitions have been calculated to be f= 0.001 for both XeF2 and XeF4. The vibronic band in XeF2 borrows intensity from the symmetry allowed 1A1g→1A2u transition at 1580Å (f=0.45), while in XeF4 the major contribution to the vibronic band is from the symmetry allowed 1A 1g→1Eu transition at 1325 Å (f=0.8). A temperature dependence of the intensity of the 2330 Å band in XeF 2 has been observed and found to be less than that predicted by the Herzberg-Teller theory. The estimated strength of the singlet-triplet transition in XeF2 corresponding to the singlet-singlet transition at 1580 Å is shown to be small (f≦ 10-4) in spite of a heavy atom effect; the small transition strength persists because of the lack of nearby excited states of the required symmetry. In XeF4 the triplet excited state 3Eu corresponding to the singlet-singlet transition 1A1g→1Eu at 1840Å (f=0.22) is permitted by group theoretical selection rules to mix with its own singlet state. Using an intermediate coupling scheme the estimated intensity of this singlet-singlet transition is calculated to be f=0.007. The theoretical estimates of the symmetry and spin forbidden transition strengths are used for the assignment of the weak electronic transitions in the xenon fluorides.