An oxirane compound is prepared by reacting an olefinically unsaturated compound with hydrogen peroxide in the presence both of (i) at least one lead compound, exemplarily triethyl lead hydroxide and also of (ii) at least one compound of a group IV-A, V-A or VI-A transition metal exemplarily tungsten hexacarbonyl. The epoxided products are useful in the manufacture of plastics, adhesives and the like.