Process for manufacturing an oxirane by reaction between an olefin and a peroxide compound in a reactor containing a liquid phase, in the presence of water, one or more organic solvents, a catalyst and one or more compounds for increasing the selectivity of the catalyst toward epoxidation reactions, in which: if the process is performed in batchwise mode, the liquid phase present in the reactor when the reaction starts, if the process is performed continuously, all of the liquid phases that are fed continuously into the reactor has/have a total organic solvent content of at least 0.1 g/kg and of not more than 675 g/kg.