Spectral classifications in the near infrared of stars with composite spectra. III. Study of a sample of 137 objects with the Aurelie spectrograph We provide spectral classifications for a sample of 137 stars mentionedas having composite spectra. The classifications were carried out on 33Angstroms /mm spectra in the region 8370 - 8870 Angstroms. Of these 137objects, 115 correspond in the infrared to cool stars (G, K or M) ofluminosity classes III, II and I; for 22 stars, we find only hot spectraof types B, A, F or Am, so that they do not fulfil our definition ofcomposite spectra. We detect four new Am stars, and one Am star (HD70826) turns out to be a composite spectrum object. As in Paper II, thecool components of composite spectra show a strong concentration in thevicinity of G8III. Based upon observations carried out at Observatoirede Haute-Provence (OHP).