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The complex permittivity of bulk crystals of semiinsulating gallium arsenide (GaAs) and gallium phosphide (GaP) were measured over the frequency range from 4 to 30 GHz and at temperatures from 30 up to 300 K employing whispering-gallery-mode (WGM) and quasi-TE0 np-mode dielectric-resonator techniques. At temperatures about 40 K, dielectric loss tangent values were below 10 -6 for GaAs and below 10 -5 for GaP. The use of several WGMs, as well as TE0 np modes excited in the same test sample enabled a broad frequency range of measurements (one decade). The real part of the permittivity of GaP and GaAs proved to be frequency independent at microwave frequencies. The dielectric loss tangents of GaAs and GaP increase with temperature and frequency.