We report microphotoluminescence studies of GaN/AlN quantum dots grown along the (0001) crystal axis by molecular‐beam epitaxy on sapphire substrates. To obtain quantum dots with different density and size a nominal GaN coverage was varied from 1 to 4 monolayers. The highest density of quantum dots was about 1011 cm‐2, so about 103 quantum dots was excited in experiments. We found that the photoluminescence intensity of a sample with the smallest amount of deposited GaN decreases in more than two orders of magnitude under continuous‐wave laser exposure during about 30 minutes and then it remains stable. The photoluminescence intensity of the rest samples was time‐independent quantity. The emission band of the former sample exhibits a prominent linear polarization along the growth plane. We assume that the quite high degree of polarization can be due anisotropy of strain and/or shape of the quantum dots formed near dislocations which act also as recombination centers causing photoluminescence quenching. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)