[en] Time-Dependent Convection (TDC) models obtained by combining the local treatment of Gabriel (1996) and Grigahcene et al. (2005) and the non-local prescriptions of Spiegel (1963) are presented. We show that in the stationary unperturbed case, these non-local treatments can be constrained by the results of 3D hydrodynamic simulations (Stein & Nordlund 1998). We consider here the case of solar-type stars with a large convective envelope and A-F type stars with two very thin surface convection zones.