Our photometric–hydrodynamic method is generalized to determine the fundamental parameters of multiperiodic radially pulsating stars. We report 302 UBV(RI)C Johnson–Kron–Cousins observations of GSC 4868–0831. Using these and the published photometric data of V372 Ser, we determine the metallicity, reddening, distance, mass, radius, equilibrium luminosity and effective temperature. The results underline the necessity of using multicolour photometry, including an ultraviolet band, to classify the subgroups of RR Lyrae stars properly. Our U observations might reveal that GSC 4868–0831 is a subgiant star pulsating in two radial modes and that V372 Ser is a giant star with the size and mass of an RRd star.