An interpretation is given of the broadened EPR spectra of Gd3+ ions, which are frequently observed in polycrystalline ceramics and glasses. A reasonable simulation of the spectra is obtained, when these are regarded as a superposition of a large number of normal EPR powder spectra, each of which can be described with the usual spin-Hamitonian. These originate from the many different surroundings of the Gd3+ ions in these compounds due to the structural disorder. The result is, that only those transitions, which are independent of the zero field splitting parameters in the spin Hamiltonian, remain visible in the derivative spectrum. The interpretation is supported by the EPR powder spectrum of the Gd3+ doped compound CaHf4O9, which changes from broadened into clearly resolved, when the compound is ordered by an annealing process.