  In this talk we discuss the process e^+e^-\to t\bar t near threshold,
calculated with NNLO accuracy as well as top quark mass definitions adequate
for the threshold. As new definition we suggest the PS-bar mass which allows to
calculate recoil corrections to the static PS mass. Using this result we
calculate the cross section of e^+e^-\to t\bar t near threshold at NNLO
accuracy adopting three alternative approaches, namely (1) fixing the pole
mass, (2) fixing the PS mass, and (3) fixing the new mass which we call the
PS-bar mass. We demonstrate that perturbative predictions for the cross section
become much more stable if we use the PS or the PS-bar mass for the
calculations. A careful analysis suggests that the top quark mass can be
extracted from a threshold scan at NLC with an accuracy of about 100 MeV.
