At present, the most general evolutionary theory of honest communication is Grafen's model of Zahavi's ‘handicap’ signalling system, in which honesty of signals about the signaller's quality (e.g. mate suitability or fighting ability) is maintained by the differentially high cost of signals to signallers having lower quality. The latter model is here further generalized to include any communication between signallers and receivers that are genetically related (e.g. parents and begging offspring, cooperative or competing siblings). Signalling systems involving relatives are shown to be evolutionarily stable, despite a potential pay–off for false signalling, if the Zahavian assumption of differential signal costs holds and there are diminishing reproductive returns to the signaller as the receiver's assessed value of its attribute increases, or if, regardless of whether the Zahavian assumption holds, signallers with high values of the attribute benefit more from a given receiver assessment than signallers with low values (e.g. begging chicks that are hungrier benefit more from being fed). In stable systems of signalling among kin, it is also shown to be generally true that (i) levels of signalling and thus observed signal costs will decline as relatedness increases or as the receiver's reproductive penalty for erroneous assessment increases, and (ii) receivers will consistently, altruistically overestimate the true value of the signalled attribute.