Experiments show that polymer melt extrusion processes can exhibit pressure oscillations which are called spurt. This paper focuses on different models for these pressure oscillations. Three models are compared. Model A with a well-chosen slip law is investigated for a qualitative description of spurt. Model B uses the nonlinear Johnson-Segalman-Oldroyd constitutive equation to describe the pressure-controlled extrusion with non-slip boundary conditions. Model C, also with non-slip boundary conditions, deals with two concentric Newtonian flow regions in the die, where the outer region is very thin and has much lower viscosity than the inner region. The invesigation leads to the conclusions: the models A and C can successfully describe all experimental observations of the spurt phenomenon, while the model B fails. The wall slip approach and a boundary layer approach do equally well in describing spurt.