The electron and hole intraband spectroscopy in GaSe nanoparticles having diameters ranging from 4 to 9 run is studied by femtosecond transient absorption polarization methods. The results indicate that the transient absorption spectrum in the 500-700 nm region has a size-independent peak at about 600 nm. Polarization results indicate that the absorption anisotropy is small or negative on the blue edge of the spectrum and increases with increasing wavelength. The anisotropy reaches a maximum in the 600 nm region and remains approximately constant out to 700 nm. Smaller particles exhibit smaller (or more negative) anisotropies and a larger wavelength dependence than larger particles. These results are interpreted in terms of a simple effective mass model. Due to the approximately cylindrical symmetry of these two-dimensional particles, the electron and hole states are described by particle-in-a-cylinder wave functions and the optical transitions may be calculated from these wave functions. These calculations semiquantitatively predict the absorption maximum at 600 nm and qualitatively predict the wavelength dependence of the absorption polarization. They are also consistent with the size dependence of the anisotropy spectrum. Absorption near the 600 nm maximum is assigned to an out-of-plane hole intraband transition, while the transient absorptions to the blue of the maximum are assigned to in-plane electron and hole intraband transitions. The observation of a positive anisotropy at the longest wavelengths suggests the presence of a weak underlying, z-polarized electron intraband transition at redder wavelengths. These assignments are consistent with the previously reported studies indicating that the absorption is largely quenched in the presence of the hole acceptor, pyridine.