In heterogeneousnetworks sending messagesmay incur different delayson different edges,and eachprocessormay havea different switching timebetweenmessages.Thewell studiedTelephonemodelis obtainedwhenall edgedelaysandswitching times areequalto oneunit. We investigatethe problem of finding the minimum time required to multicast a messagefrom one sourceto a subsetof the processorsof size k. The problem is NP-hardevenin the basic Telephonemodel.Wepresentapolynomial timealgorithmthatapproximatestheminimummulticasttimewithin afactorof O(log k). Ouralgorithmimprovesonthebestknownapproximationfactorfor theTelephonemodelby afactorof 0 (e). No approximation algorithmswere known for the generalmodel consideredin this paper.