The Tokaj Mountains is the easternmost of the Miocene volcanic ranges in Hungary. The volcanic pile mainly consists of andesitic and rhyolitic rocks, but the dacitic types are also important. The banded, quartz-containing dacite of Tokaj-Nagyhegy is one of the most interesting rock in the mountain range. In the interpretation of this paper, the mixing of andesitic and rhyolitic magmas played the main role in the genesis of the dacite. The diorite-porphyrite inclusions in the dacite can be derived from an andesitic melt, whereas the dihexahedral quartz crystals are relicts of a rhyolitic material. The numerical determination of the rhyolite/andesite admixture has been also attempted.