In the stoichiometric asymmetric epoxidation of E-beta-methylstyrene with cationic chromium-salen oxo complexes, enantioselectivity is elevated by the addition of many different types of phosphoryl compounds. Triarylphosphine oxides are the most effective. and, amongst them,, tris(3,5-dimethylphenyl)phosphine oxide gave the highest ee to date (93%). There is a ceiling effect of additive. bulky additives are ineffective, there is no substituent electronic effect within the additive and there is a saturation of its effect with increasing concentration. (C) 2002 Elsevier Science Ltd. All rights reserved..