The dielectric function and momentum relaxation time of carriers for a single-crystal GaSe were investigated using terahertz time-domain spectroscopy over the frequency range from 0.4 to 2.4 THz. The key parameters determined from THz data using the Drude model are: the plasma frequency ωp = 6.1 ± 0.5 THz, the average momentum relaxation time <τ> = 51 +± 6 fs for electrons. The THz absorption spectrum showed resonance structures attributed to the difference frequency combinations associated with acoustical and optical phonons. This paper has already been published, see B. L. Yu, F. Zeng, V. Kartazayev, and R. R. Alfano, “Terahertz studies of the dielectric response of and second order phonons in a GaSe crystal,” Appl. Phys. Lett. 86, 182104 (2005).