An electrosurgical system includes an electrosurgical generator (1) including at least one source of radio frequency (RF) power, and a plurality of output connections (2, 3, 4), only one of the output connections at any one time being active in that it is able to receive radio frequency power from the source. The generator (1) includes selection means adapted to change the active output connection, and a controller adapted to control the supply of radio frequency power from the source to the active output connection. The system also includes a plurality of electrosurgical assemblies, each including an electrosurgical instrument (5, 6, 7) and a cable (8, 9, 10) connecting the electrosurgical instrument to one of the output connections (2, 3, 4). The electrosurgical instruments (5, 6, 7) each include a handswitch (17, 18, 19) adapted to send a signal to the generator (1) to change the active output connection. The selection means is such that a signal sent from the handswitch (17, 18, 19) of the active instrument (5, 6, 7) can cause the generator (1) to change the active output connection to a different output connection (2, 3, 4), but a signal sent from the handswitch of an instrument other than the active instrument does not immediately cause the selection means to change the active output connection to a different output connection.