We present high-resolution (R approximately 300-600) infrared (1.0-3.4-mu-m) spectra of a sample of Wolf-Rayet stars of subtypes WC5-9. The line identifications are thoroughly discussed and some 20 new identifications given, notably the C IV 4p-4s doublet at 1.435-mu-m, observed previously but not identified, He I 5p-3d (at 1.299-mu-m), He II 17-7 (at 1.344-mu-m), He II 16-7 (at 1.381-mu-m) and He II 14-9 (at 3.145-mu-m). We also identified satellite lines of the C IV 10-9, 9-8 and 8-7 and C III 7-6 arrays, several other lines of C III and lines of oxygen (O III, OV, O VI). The 2p-2s He I lines present P Cygni profiles, the absorption component of the triplet (1.083-mu-m) being stronger in earlier subtypes and the singlet (2.058-mu-m) in later subtypes. We show that the infrared features, in particular the helium lines, can be used to identify the WC subtypes and to help understand the physical meaning of their spectral differences. We find that the spectrum of WR 146 is anomalous: the degree of ionization and the carbon features indicate a WC6 subtype, the linewidths a WC4, and the strong helium and weak oxygen features a WC8.