In this paper we analyse the superconvergence property of the streamline diffusion finite element method (SDFEM) in the case of elliptic problems with characteristic layers. For the SDFEM we give optimal parameter choices for maximal stability in the induced streamline diffusion norm. It is shown that inside the parabolic boundary layer the SDFEM-parameter can be chosen of order ε^{- 1 / 4} N^-2 which is also confirmed by numerical results.