We apply for the first time time-dependent convection (TDC) models to the study of the driving mechanism of the Pulsating DB (V777 Herculis) white dwarfs. From the blue to the red edge of the instability strip of these stars, TDC appears to play a central role in the driving. Around the blue edge, the convection adapts quasi-instantaneously to the oscillations, so that TDC must be included in the models. For the first time, we show that the red edge of the DB instability strip is successfully obtained with a TDC treatment, especially thanks to the terms due to the turbulent pressure variations, while it is not reproduced with frozen convection models.