Abstract.A detailed spectroscopic study of 11 giants with spectral type from G9 to M2 is presented. The 2.38-4.08 µm wavelength-range of band 1 of ISO-SWS (Short-Wavelength Spectrometers on board of the Infrared Space Observatory) in which many different molecules -with their own dependence on each of the stellar parameters -are absorbing, enables us to estimate the effective temperature, the gravity, the microturbulence, the metallicity, the CNO-abundances, the 12 C/ 13 C-ratio and the angular diameter from the ISO-SWS data. Using the Hipparcos' parallax, the radius, luminosity and gravity-inferred mass are derived. The stellar parameters obtained are in good agreement with other published values, though also some discrepancies with values deduced by other authors are noted. For a few stars (δ Dra, ξ Dra, α Tuc, H Sco and α Cet) some parameters -e.g. the CNO-abundances -are derived for the first time. By examining the correspondence between different ISO-SWS observations of the same object and between the ISO-SWS data and the corresponding synthetic spectrum, it is shown that the relative accuracy of ISO-SWS in band 1 (2.38-4.08 µm) is better than 2% for these high-flux sources. The high level of correspondence between observations and theoretical predictions, together with a confrontation of the estimated T eff (ISO) value with T eff values derived from colours -which demonstrates the consistency between V − K, BC K , T eff and θ d derived from optical or IR data -proves that both the used models to derive the stellar quantities and the flux calibration of the ISO-SWS detectors have reached a high level of reliability.