An assemblage of alunite-supergroup minerals (ASM), rhabdophane-group minerals (RGM), goethite and associated clay minerals occurs in Permian A-type porphyritic microgranite in the eastern part of the Velence Hills, Hungary. The secondary sulfates/phosphates include jarosite, Pb-rich jarosite and alunite, corkite, hinsdalite and rhabdophane-(Ce), -(La) and -(Nd). Detailed electron probe microanalysis and Raman spectroscopy reveal a wide miscibility among RGM end-members and show a rhabdophane–tristramite–brockite solid solution with extensive compositional variation. Moreover, ASM show heterogeneous composition and complex substitution mechanisms within the alunite, beudantite and plumbogummite groups. The formation of this rare mineral assemblage reveals extensive remobilization of rare-earth elements (REE), Th, U, P, S, Fe and Pb under supergene conditions. Compositional variations and substitution trends of the RGM investigated indicate that Th, U, Ca and Pb are incorporated into the rhabdophane structure by a (Ca, Pb)2+ + (Th, U)4+ ↔ 2REE3+ substitution mechanism. Consequently, we suggest the following end-member formulae for RGM containing divalent and tetravalent cations: (Ca0.5Th0.5)PO4·H2O for brockite, (Pb0.5Th0.5)PO4·H2O for grayite and (Ca0.5U0.5)PO4·2H2O for tristramite. The ASM and RGM originated from total leaching of the primary magmatic REE, Th, U and P minerals in the microgranite [most probably allanite-(Ce), fluorapatite and possibly also xenotime-(Y)], together with input of Pb and S in low-temperature, acid sulfate solutions, connected with an adjacent Palaeogene andesite–diorite intrusion and the accompanying hydrothermal sulfide mineralization.