We have started a high resolution optical observation program dedicated to the study of chromospheric activity in weak-lined T Tauri stars (WTTS) recently discovered by the ROSAT All-Sky Survey (RASS). It is our purpose to quantify the phenomenology of the chromospheric activity of each star determining stellar surface fluxes in the more important chromospheric activity indicators (Ca II H & K, H_beta, H_alpha, Ca II IRT) as well as obtain the Li I abundance, a better determination of the stellar parameters, spectral type, and possible binarity. A large number of WTTS have been discovered by the RASS in and around differen star formation clouds.Whether these stars are really WTTS, or post-TTS, or even young main sequence stars is a matter of ongoing debate. However, we have centered our study only on objects for which very recent studies, of Li I abundance (greater than Pleiads of the same spectral type) or radio properties, clearly confirmed their pre-main sequence (PMS) nature. In this contribution we present preliminary results of our January 1998 high resolution echelle spectroscopic observations at the 2.1m telescope of the McDonald Observatory. We have analysed, using the spectral subtraction technique, the H_alpha and Ca II IRT lines of six WTTS (RXJ0312.8-0414NW, SE; RXJ0333.1+1036; RXJ0348.5+0832; RXJ0512.0+1020; RXJ0444.9+2717) located in and around the Taurus-Auriga molecular clouds. A broad and variable double-picked H_alpha emission is observed in RXJ0444.9+2717. Emission above the continuum in H_alpha and Ca II IRT lines is detected in RXJ0333.1+1036 and a filling-in of these lines is present in the rest of the stars. Our spectral type and Li I EW deterninations confirm the PMS nature of these objects.
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