Electrosurgical forceps in which one or more pairs of non-resonant unbalanced lossy transmission line structures are arranged on the inner surfaces of the jaws of the forceps provide both (i) active and return electrodes for a radiofrequency (RF) signal, and (ii) lossy structures for delivering a microwave signal into biological tissue in conjunction with a mechanical gripping arrangement for applying pressure to material held within the jaws. The location of the pairs of transmission lines on the jaws of the forceps and the selection of the material of the jaws is arranged to ensure that any biological tissue gripped by the jaws become the propagation medium for the RF signal and the medium into which the microwave signal is lost.