The discovery of hundreths of X-ray emitting stars possibly associated with pre-main sequence (PMS) low-mass stars far from molecular clouds, makes it necessary to adopt quantitative spectroscopic criteria for classifying them. T Tauri stars have young ages (<10Myr) and low masses (M<2Msun_). As a consequence, it is shown that they must verify two spectroscopic conditions: (1) spectral type in the range K0-M6, and either (2a) strong emission lines and UV-optical-NIR continuum excesses, or (2b) weak-emission lines and a photospheric LiIλ670.8 absorption feature with a "minimum" equivalent width which depends on its spectral type. Classical T Tauris meet criteria (1) and (2a), while weak T Tauris (WTTS) meet criteria (1) and (2b). T Tauri stars occupy a different region in the T_eff_-W_LiI_ diagramme than the low-mass members of young open clusters. Post T Tauri stars (PTTSs) later than about K2 can be clearly identified in the same diagramme because they fill an empty region (PTT-gap), intermediate between the T Tauris and the young cluster stars. The application of the spectroscopic criteria defined in this work to the PMS stars claimed to have been discovered in recent X-ray surveys of molecular clouds is hampered by the lack of high-resolution optical spectra for most of them. On the basis of the sparse and modest-resolution data that is available, the preliminary results indicate that the majority of these stars (~60%) are not WTTSs. Only ~25% of the non-WTTS X-ray discovered stars are clearly PTTSs according to this study. The PMS status of the remaining stars is dubious. It seems unlikely that the PTTSs indentified in X-ray surveys outnumber the T Tauri stars. Far away from molecular clouds, the number of WTTSs and PTTSs appear to decrease significantly.