  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.
