This paper presents the analysis of near-infrared observations of the icy surface of Triton, recorded on 1995 September 7, with the cooled grating spectrometer CGS4 at the United Kingdom Infrared Telescope (Mauna Kea, HI). This analysis was performed in two steps. The first step consisted of identifying the molecules composing Triton's surface by comparing the observations with laboratory transmission spectra (direct spectral analysis); this also gives information on the physical state of the components. Most of the bands in Triton's spectrum were assigned to specific vibration bands of the CH 4 , N 2 , CO, and CO 2 molecules previously discovered. A detailed comparison of the frequencies of the CH 4 bands confidently indicated that this molecule exists in a diluted state in solid β-N 2 . Three new bands peaking at 5717, 5943, and 6480 cm -1 (1.749, 1.683, and 1.543 µm, respectively) were also observed. Laboratory experiments have shown that C 2 H 6 isolated in solid N 2 fits well the second band, but this would imply the appearance of unobserved bands and thus rules out this assignment. However, C 2 H 6 may exist in another physical state, and more experiments are necessary. No plausible candidate was found for these three bands when comparing with the spectra of nine molecules (C 2 H 2 , C 2 H 4 , C 3 H 8 , NH 3 , SO 2 , HC 3 N, CH 3 OH, NO, NO 2 ). In view of the results of D. P. Cruikshank et al. (1993, Science 261, 742; in preparation), the work presented here leads to two possible representations of the surface of Triton. First, a two-region surface composed of a N 2 : CH 4 : CO terrain, N 2 : CH 4 : CO consisting of a solid solution in which N 2 is the dominant molecule, and of a H 2 O + CO 2 terrain, composed of a mixture of pure crystalline H 2 O and CO 2 grains. The second representation is a three-region surface composed of a N 2 : CH 4 : CO terrain and two geographically separated H 2 O and CO 2 terrains. The second step of the analysis consisted of using a bidirectionnal reflectance model (S. Douté and B. Schmitt 1998, J. Geophys. Res. Planets 103, 31367). The modeling first confirms the direct spectral analysis in that CH 4 is diluted in solid β-N 2 , giving a high degree of confidence to the conclusion that the N 2 : CH 4 : CO terrain is in fact a solid solution. It also provides numerical information on this terrain, namely the size of the grains, the geographical abundance, and the CH 4 and CO concentrations. The large grain size (around 10 cm) would mean that the texture of this terrain is a compact crystalline solid rather than granular, which is in agreement with calculations