Highly resistive GaN: Be was obtained by means of synthesis of Ga+Be with atomic nitrogen under high nitrogen pressure. Activation energy of resistivity is about 1.5eV. This material exhibits features very different from those observed in highly resistive bulk GaN : Mg. Up to 300 K strong yellow band dominates photoluminescence spectrum in resistive GaN:Be crystals. Positron annihilation studies point to the presence of gallium vacancies, V-Ga.In highly resistive GaN:Mg neither yellow band with considerable intensity, nor detectable concentration of V-Ga was found. We also discuss the puzzling findings in highly resistive bulk GaN : Be of morphological features typical for highly conducting bulk n-GaN material.