  A model based on a nonrelativistic potential supplemented by spin dependent
terms of the Breit-Fermi type is described. This model reproduces the known
masses of the $\bar{b}b$ quarkonia within 1MeV and the known masses of the
$\bar{c}c$ quarkonia within 5MeV. Many predictions are made, some of them, e.g.
for the fine splittings of the high $L$ states of the $\bar{b}b$ quarkonia and
of the mass spectrum of the $\bar{b}c$ quarkonia, significantly different from
previous predictions made by other authors.
