We present proper motions of 72 T Tauri stars located in the central region of Taurus-Auriga (Tau-Aur). These proper motions are taken from a new proper motion catalogue called STARNET. Our sample comprises 17 classical T Tauri stars (CTTS) and 55 weak-line T Tauri stars (WTTS), most of the latter discovered by ROSAT. 53 stars had no proper motion measurement before. Kinematically, 62 of these stars are members of the association. A velocity dispersion of less than 2-3km/s is found which is dominated by the errors of the proper motions. This velocity dispersion correlates with a spread in distances. Furthermore we present proper motions of 58 stars located in a region just south of the Taurus molecular clouds and compare the kinematics of the youngest stars in this sample (younger than 3.5x10^7^yrs) with the kinematics of the pre-main sequence stars (PMS) in the Taurus-Auriga association. From a comparison of the space velocities we find that the stars in the central region of Tau-Aur are kinematically different from the stars in the southern part. Among the stars with large proper motions far off the Taurus mean motion we find 2 Pleiades candidates and 7 possible Pleiades runaway stars.