There has been continuing effort to understand the cause for the thickness dependence observed in the glass transition dynamics of polymer films. In a previous experiment, we showed that a two-layer model, assuming the films to contain a high-mobility surface layer residing on top of a bulklike inner layer, can explain the thickness dependence found in the viscosity of unentangled polystyrene films. Here, we examine the validity of this model in polystyrene films that are entangled. Unlike the unentangled films, the entangled ones are initially out-of-equilibrium, exhibiting a plateau modulus similar to 1/10 times the bulk value. Upon annealing, the viscosity typically grows with time and eventually saturates. For the films with thickness above 20 nm, the saturated viscosity is the same as the bulk and takes similar to 5-10 reptation times to reach. We find that the saturated viscosity is fully explainable by the two-layer model. A straightforward interpretation would imply that the surface mobile layer exists at equilibrium and modifies the dynamics of unentangled and entangled polymer films in a similar way.