The red giant and supergiant region in the Herzsprung-Russell Diagramme displays different branches. All stars in this region have stellar activity and mass loss in common, however the degree or rate of these characteristics varies significantly between the giant branches, namely the First Giant Branch (FGB), the Horizontal Branch and the Asymptotic Giant Branch (AGB). The aim of this proposal is 1) to explore systematically molecular bands in giants and supergiants at different stages of stellar evolution, 2) to establish a diagnostic tool based on molecular bands from optically well studied giants, and 3) to establish the link between early phases of the giant evolution and the AGB phase. The impact of spectral type, luminosity and physical and chemical conditions of the outer atmosphere on the molecular bands will be analysed and correlated with observational results from UV and optical observations. To achieve this, a sample of cool giants and supergiants, which covers spectral types between K3 and M9, and all types of stellar activity, from a quiescent atmosphere, via variable chromospheres to pulsation dominated atmospheres. OBSERVATION SUMMARY The bulk of molecular bands and dust features fall into the SWS wavelength region; in particular wator vapor, and most diatomic molecules. To cover these features, a full wavelength scan will be performed where a resolution of 1/8 of the nominal SWS resolution will be used. The information gained with a higher resolution spectrum does not compensate for the increase in costs of observing time. The primary features to be investigated are the fundamental and overtones of water vapor, and diatomic molecules. The spectral types cover K3 to M9 including C- type and S-type stars, of various stellar activity. The fast scanning mode of SWS will be used (SWS01) for 30 objects, with an integration time of 25 minutes each. The flux ranges and S/N ratios achieved are as follows: wavelength : min./max. flux min./max. S/N at 2 microns : 30 - 22000 Jy S/N = 110 -> 10000 at 12 microns : 7 - 4200 Jy S/N = 40 -> 3000 at 25 microns : 2 - 1000 Jy S/N = 20 -> 1500 at 45 microns*: 1 - 500 Jy S/N = 5 -> 400 (* interpolated from IRAS fluxes) Thus a high enough S/N ratio will be achieved in the wavelength domain of bands of diatomic molecules and water vapor, i.e between 2 and 15 microns. Including 20% of the time for instrument overheads and 3 minutes per observation for target acquisition and pointing, 33 minutes per object are needed.