The spectra of heavy quarkonia are studied in two approaches: with the use of the Afonin-Pusenkov representation of the Regge trajectory for the squared excitation energy E 2 (nl) (ERT), and using the relativistic Hamiltonian with the universal interaction. The parameters of the ERTs are extracted from experimental mass differences and their values in bottomonium: the intercept a(bb) = 0.131 GeV 2 , the slope of the orbital ERT b l (bb) = 0.50 GeV 2 , and the slope of the radial ERT, bn(bb) = 0.724 GeV 2 , appear to be smaller than those in charmonium, where a(cc) = 0.381 GeV 2 , b l (cc) = 0.686 GeV 2 , and the radial slope bn(cc) = 1.074 GeV 2 , which value is close to that in light mesons, bn(qq) = 1.1(1) GeV 2 . For the resonances above the DD threshold the masses of the χc0(nP ) with n = 2, 3, 4, equal to 4218 MeV, 4503 MeV, 4754 MeV, are obtained, while above the BB threshold the resonances Υ(3 3 D1) with the mass 10693 MeV and χ b1 (4 3 P1) with the mass 10756 MeV are predicted.