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This work is part of a larger project on the study of activity in stars of spectral type similar to, or later than the Sun, from PMS to ZAMS, based on the analysis of the high resolution CaII InfraRed Triplet (CaII IRT: λ= 8498, 8542, 8662Å) observed profiles. Here, a preliminary study on the diagnostic power of these calcium lines has been performed by means of NLTE calculations of the line profiles with an approximate treatment of UV line-blanketing, for a grid of photospheric models with T_eff=4200, 5200, 6200K, logg=4.0, 4.5, 5.0 and [A/H]=0.0, -1.0, -2.0. We used these calculations to estimate the sensitivity of the profiles to changes in stellar parameters and the effect of departures from LTE. As found by other authors, the CaII triplet NLTE EQWs (equivalent widths) are quite sensitive to photospheric parameters, in particular to T_eff and [A/H]. On the other hand, we find that the dependence of the CaII triplet lines central depression (CD=1-central relative flux) on logg and T_eff, and to a lesser extent to [A/H], is very weak. The departure from LTE is negligible when we consider EQWs, unless very metal-poor atmospheres are considered, while CDs can be affected by NLTE by more than 20%. This analysis indicates that in the use of these lines as activity indicators (where the details of the line profile in the core are important), a NLTE treatment is required. Furthermore, we show that a new chromospheric indicator, which we denote R_IRT, can be derived from measurements of CaII IRT line central depressions, provided that rotational broadening is taken into proper account. In order to facilitate the use of the CaII IRT lines as activity diagnostics, we give interpolation formulae for estimating line CDs within the range of stellar parameters of our NLTE calculations.