We review briefly the basic properties of the GW Vir stars and of the V777 Her stars. We describe the classical kappa-mechanism operating in the GW Vir stars and the effects of the chemical composition and of the interaction between diffusion and mass loss on the boundaries of the instability domain of these objects in the log g - T[SUB]eff[/SUB] diagram. Because of the presence of an extensive superficial convection zone in pulsating DB (V777 Her) white dwarfs, oscillation modes are not excited through a similar classical kappa-mechanism in those stars but, instead, involve pulsation-convection interactions. We describe the effects of a time-dependent convection (TDC) treatment on the driving mechanism of the V777 Her stars. We show how convection deeply affects the excitation of modes via the entropy transport mechanism or S-mechanism. Provisional blue and red edges are calculated for the V777 Her stars and are found at T[SUB]eff[/SUB] ~= 28,500 K and ~= 20,500 K, respectively, for a 0.6 M[SUB]o[/SUB] star under the assumption of ML2 convection.