Electric monopole transitions between the 0~-, 0~-and 23, 2~-levels in 768e, populated in the decay of 76Br, were investigated by means of conversion electrons and gammaray spectroscopy. The K-electron intensity ratios of E0 and E2 transitions connecting the 0 + level to the 0[ and 2 + levels and of the E0 and E2 components in the 2 + ~2~-transition were determined. The ratio X(EO/E2) of the E0 to E2 reduced transition probabilities and, from the available lifetimes, the E0 strength parameters p(EO) were deduced for the two transitions. The results are compared with the predictions of current models.