On beam tests were carried out on PbW04 crystals. One of the aims of this work was to evaluate the contribution of the Cerenkov component to the total light yield. The difference in the timing characteristics of the fast Cerenkov signals with respect to the scintillation ones, which are emitted with a decay time of about 10 ns, can be exploited in order to separate the two proportions. In this paper we present the results of an analysis performed on the time structure of signals, showing how it is possible to detect and assess the presence and the amount of Cerenkov light. Since Cerenkov light is emitted only by the electromagnetic component of a hadronic shower, its precise measurement would allow to account for one of the dominant sources of fluctuations in hadronic showers and to achieve an improvement in the energy resolution of a hadronic calorimeter.