The second flight of Stratoscope II was carried out during the night of November 26,1963. The telescope was equipped with an infrared spectrometer with a useful sensitivity range from 1 to 3 M The balloon operations were carried out without difficulty. The telescope was operated from 6 P.M to 6 A.M. Spectral tracings were obtained for ten objects. This paper reports on the observations of six nearby red- giant stars. The spectra of the hotter objects showed that the terrestrial atmosphere above the balloon had no disturbing effects on the measurements. The only terrestrial band weakly indicated in the spectra is that of carbon dioxide at 2.7 . The spectrum of a Tau (KS) shows practically no bands but has a clear intensity peak around 1.6 where bound-free and free-free absorption of H- and H2- leaves a relatively transparent region in the continuous absorption . The same phenomenon is shown in the spectra of the cooler stars although complicated by band structure. Water-vapor absorption bands at 1.4 and 1.9 appear distinctly in the spectrum of the supergiant a Ori (M2). These bands occur with a similar strength in the spectrum of p Per (M4), but are weaker in M Gem (M3). In the spectrum of R Leo (M8, m = 7.9) and particularly of o Cet (M9, m = 8.4) the water-vapor bands at 1.4,1.9, and 2.7 are extremely strong.