Relative rates were measured for the heterogeneous epoxidation of olefins with urea-hydrogen peroxide (UHP) in CDCl3 catalyzed by MeReO3 on Nb2O5. The rates are more selective than those in homogeneous MTO-H2O2 solutions. The reactivity orders among the alkenes are cis > trans and electron-rich > electron-poor. A molecular structure has been proposed for the active rhenium species which allows the rate differences lobe explained in terms of energy gap between the alkene occupied pi(C-C) and unoccupied sigma*(O-O) of the peroxorhenium moiety. (C) 2003 Elsevier B.V. All rights reserved.