This paper provides a detailed analysis of transient gain dynamics in saturated Raman amplifiers fed by wavelength division multiplexed (WDM) signals. Such dynamics are due to a pump saturation effect, known as pump-mediated signal-to-signal crosstalk, which is equivalent to the well-known cross-gain modulation in EDFAs. We provide for the first time a simple block-diagram model of the Raman amplifier, whose state is represented by the relative pumps depletion sensed by the signals. With such model, we are able to prove that the time constants of the Raman gain transients are of the same order as the pump–signal walk-off times. For counter-propagating pumps, the model is very accurate in predicting both the steady-state gain and the transient gain dynamics, with more than an order of magnitude improvement in computation time with respect to the direct solution of the signals and pumps propagation equations. The value of such model is therefore in the simulation of dynamic WDM networking scenarios in which the input powers have large swings in time. The model also extends to the co-propagating pump and well captures the time constants involved in the transients, although the accuracy in the predicted power levels is worse than that of the counter-propagating pump case.