  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
$a(b\bar b)=0.131\,$GeV$^2$, the slope of the orbital ERT $b_l(b\bar b)
=0.50$\,GeV$^2$, and the slope of the radial ERT, $b_n(b\bar
b)=0.724$\,GeV$^2$, appear to be smaller than those in charmonium, where
$a(c\bar c)=0.381$\,GeV$^2$, $b_l(c\bar c)=0.686$\,GeV$^2$, and the radial
slope $b_n(c\bar c)= 1.074$\,GeV$^2$, which value is close to that in light
mesons, $b_n(q\bar q)=1.1(1)$\,GeV$^2$. For the resonances above the $D\bar D$
threshold the masses of the $\chi_{c0}(nP)$ with $n=2,3,4$, equal to 4218\,MeV,
4503\,MeV, 4754\,MeV, are obtained, while above the $B\bar B$ threshold the
resonances $\Upsilon(3\,^3D_1)$ with the mass 10693\,MeV and
$\chi_{b1}(4\,^3P_1)$ with the mass 10756\,MeV are predicted.
