We propose to observe fundamental bands of CO and SiO in the infrared spectra of selected cool evolved stars by the highest resolution of the grating mode of ISO SWS. Our objective is to analyze the band structures of these molecules to clarify the physical structure of the upper atmosphere and inner circumstellar envelope of these stars. Understanding the physical structure of the upper photosphere-inner circumstellar boundary region is of essential importance to resolve such critical problems as mass-loss mechanism, formation of circumstellar dust/molecules, excitation mechanism of stellar masers, etc., since these phenomena mostly take place in the circumstellar envelope close to the stellar surface. The fundamental bands of CO and SiO may be the most important proves of the upper photosphere - chromosphere boundary, because of their high opacity. We hope to clarify the behaviour of CO and SiO fundamentals in the sequence of K-M giants and some supergiants, and further explore the changes of these bands during the pulsation of Mira variables. As we have already studied in some details the overtone bands of CO and SiO by the ground based high resolution spectra (see Sect.4), we hope to complete our analysis on the structure of the outer atmospheres of cool luminous stars with an analysis of the fundamental bands of CO and SiO using the unique possibility offered by the ISO. With the highest resolution possible by the SWS grating mode, we can resolve the band structures of CO and SiO (see Sect.3), and we hope to be able to extract some basic information on the physical conditions responsible to the formation of these bands.