[en] In this paper γ-detector, based on the radiofrequency (RF) phototube and recently developed fast and ultrafast scintillators, is considered for Time-of-Flight positron emission tomography applications. Timing characteristics of such a device has been investigated by means of a dedicated Monte Carlo code based on the single photon counting concept. Biexponential timing model for scintillators have been used. The calculations have shown that such a timing model is in a good agreement with recently measured data. The timing resolution of -detectors can be significantly improved by using the RF phototube. (authors)