This paper describes a tunable far-infrared (FIR) spectrometer. Tunable radiation is obtained by frequency mixing, fixed frequency FIR laser radiation and tunable microwave radiation in Schottky barrier diodes. An optically pumped laser and an HCN discharge laser are used as FIR sources and klystrons in the frequency range of 22-114 GHz as microwave sources. This yields an 85% coverage of the frequency region between 550 and 2700 GHz. Up to sixth order sidebands have been generated and used for spectroscopy. The ultimate sensitivity corresponds to a minimum detectable fractional absorption of 10- 5 at 1-s RC time. The applicability of the spectrometer in high-resolution spectroscopy of transient species has been demonstrated by the observation of spectra of OD and N2H+. New laser emissions of optically pumped CH2F2 have been found and accurate frequencies have been determined for some of them.