  We present results from molecular dynamics simulations of strictly
two-dimensional (2D) polymer melts and thin polymer films in a slit geometry of
thickness of the order of the radius of gyration. We find that the dynamics of
the 2D melt is qualitatively different from that of the films. The 2D monomer
mean-square displacement shows a $t^{8/15}$ power law at intermediate times
instead of the $t^{1/2}$ law expected from Rouse theory for nonentangled
chains. In films of finite thickness, chain entanglements may occur. The impact
of confinement on the entanglement length $N_\mathrm{e}$ has been analyzed by a
primitive path analysis. The analysis reveals that $N_\mathrm{e}$ increases
strongly with decreasing film thickness.
