The paper describes the synthesis of arithmetically symmetrical, broadbandLCfilters having prescribed amplitude response and nearly constant group delay, with particular reference to i.f. filters for radio-relay systems. These filters must suppress unwanted signals, particularly the adjacent carrier frequencies, without significantly distorting the required signal. For low distortion, the filters must have both flat amplitude and constant group-delay responses over the passband centre. Filters synthetised for 1800- and 960-channel systems have satisfied these requirements, the transfer-function design and measured characteristics of the filter for the 960-channel system being given as an example. The filters have the advantages that they can be inserted in the i.f. chain without the need for further phase equalisation, and that they give improved amplitude responses compared with conventional filter and equaliser combinations.