Spectral characteristics of quantum cascade lasers operating at about 2.5 terahertz have been investigated by means of high-resolution mixing spectroscopy. Linewidth, frequency tunability and frequency stability of the lasers were measured by mixing their radiation with radiation from a 2.5 terahertz gas laser (heterodyne mixing). The results of the homodyne mixing of different modes of the laser indicate on laser mode switching and large variations of the effective refractive index in the active medium caused by the laser drive current.