The electronic transport properties of parallel coupled single-electron transistors (SETs) at strong coupling under asymmetrical voltage bias are investigated theoretically. The binding of electrons and holes on the two islands of the coupled SETs is found to be the key element that governs the transport characteristics. The discrete nature of bound electrons and holes leads to the satellite Coulomb blockade oscillations, the current jumps, and the Coulomb staircases, all of which are distinct transport features of the coupled SETs. (C) 2000 Published by Elsevier Science Ltd.