We derive the boundary layer equations for the Phan-Thien-Tanner (PTT) fluid and the Giesekus fluid in two-dimensional creeping flow along a hat boundary for high Weissenberg numbers W. While it was show in [M. Renardy, High Weissenberg number boundary layers for the upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech., 68 (1997) 125-132] that the upper convected Maxwell fluid furnishes a boundary layer of order W-1, the PTT model furnishes a thicker boundary layer of order W-1/3, while the Giesekus model leads to a boundary layer of order W-1/2.