We report on the discovery of 15 new weak-line T Tauri stars (wTTS) south of the Taurus molecular clouds based on the large database produced by the ROSAT All-Sky Survey. High-resolution spectroscopy of 109 optical counterparts of X-ray sources has been performed to measure their radial velocities in order to verify kinematic membership to the Taurus T association. Using additional mid-resolution spectroscopy of 44 sources we find that 15 stars exhibit TTS characteristics such as weak Hα emission, Li 6708A absorption. and late spectral types. On the basis of their Lithium abundance we suspect hat these 15 new wTTS are relatively young. Seven of them have radial velocities between 12 and 21km/s, i.e. consistent with previously known TTS in Taurus molecular clouds, while other new wTTS lie up to 50pc away from regions of ongoing star formation and have radial velocities far off the mean Taurus velocity. The region populated by wTTS in the direction of Taurus extends much further south than previously assumed.