Near-infrared (NIR) spectroscopy is a somewhat underutilised technique for the study of minerals. The technique has the ability to determine water content, hydroxyl groups and transition metals. In this paper, we show the application of NIR spectroscopy to the study of selected minerals. The structure and spectral properties of two Cu-tellurite minerals graemite and teineite are compared with bismuth containing tellurite mineral smirnite by the application of NIR and infrared (IR) spectroscopy. The position of Cu2+ bands and their splitting in the electronic spectra of tellurites are in conformity with the octahedral geometry distortion. The spectral pattern of smirnite resembles graemite and the observed band at 10,855 cm-1 with a weak shoulder at 7920 cm-1 is identified as due to a Cu2+ ion. Any transition metal impurities may be identified by their bands in this spectral region. Three prominent bands observed in the region of 7200-6500 cm-1 are the overtones of water while the weak bands observed near 6200 cm-1 in tellurites may be attributed to the hydrogen bonding between (TeO3)2- and H2O. The observation of a number of bands centred at around 7200 cm-1 confirms molecular water in tellurite minerals. A number of overlapping bands in the low wavenumbers 4500-4000 cm-1 is the result of combinational modes of (TeO3)2- ion. The appearance of the most intense peak at 5200 cm-1 with a pair of weak bands near 6000 cm-1 is a common feature in all the spectra and is related to the combinations of OH vibrations of water molecules and bending vibrations ν2 (δ H2O). Bending vibrations δ H2O observed in the IR spectra show a single band for smirnite at 1610 cm-1. The resolution of this band into a number of components is evidenced for non-equivalent types of molecular water in graemite and teineite. (TeO3)2- stretching vibrations are characterised by three main absorptions at 1080, 780 and 695 cm-1.