Rhyolite volcanoes represent a substantial part of Tertiary volcanites in Carpathians and Pannonian basin. They often host epithermal and VMS mineralizations and a suite of industrial mineral and stone deposits (perlites, silicites, clays, bentonites, zeolites, pumice and stone/aggregate). Explosive eruptions of rhyolites and pyroclastic flows associated with a growth of extrusive domes represent also a serious hazard in areas of active volcanism. A greater knowledge on processes and products of rhyolite volcanism is desirable. Also for the rhyolite volcanism there is characteristic formation of monogenetic volcanic fields. The project aims at paleovolcanic reconstruction of the Tertiary monogenetic rhyolite volcanoes in Slovakia and northern Hungary, characteristics of their eruption mechanism, their evolution in time and relationship among their evolution and form on one side and basement structure and magmatic source on the other side. We shall compile a generalized model of their evolution.