A model based on a nonrelativistic potential supplemented by spin depe
ndent terms of the Breit-Fermi type is described. This model reproduce
s the known masses of the (b) over bar b quarkonia within 1MeV and the
known masses of the (c) over bar c quarkonia within 5MeV. Many predic
tions are made, some of them, e.g. for the fine splittings of the high
L states of the (b) over bar b quarkonia and of the mass spectrum of
the (b) over bar c quarkonia, significantly different from previous pr
edictions made by other authors.