In undoped high-resistivity GaN epilayers grown by metalorganic chemical vapor deposition (MOCVD) on sapphire, deep levels are investigated by persistent photoconductivity (PPC) and optical quenching (OQ) of photoconductivity (PC) measurements. The PPC and OQ are studied by exciting the samples with two beams of radiation of various wavelengths and intensities. When the light wavelengths of 300 and 340nm radiate the GaN epilayer, the photocurrent without any quenching effect is rapidly increased because the band gap transition only occurs. If the background light is 340nm and the quenching light is 564 or 828nm, the quenching of a small photocurrent generates but clearly. Two broad quenching bands that extend from 385 to 716nm and from 723 to 1000nm with a maximum at approximately 2.2eV (566nm) is observed. These quenching bands are attributed to hole trap level's existence in the GaN epilayer. We point out that the origin of the defects responsible for the optical quenching can be attributed to nitrogen antisite and/or gallium vacancy.