  An additional spheroidal integral of motion and a group of dynamic symmetry
in a model quantum-mechanical problem of two centres eZ_{1}Z_{2}omega with
Coulomb and oscillator interactions is obtained, the group properties of its
solutions being studied. P(3) \otimes P(2,1), P(5,1) and P(4,2) groups are
considered as the dynamic symmetry groups of the problem, among them P(3)
\otimes P(2,1) group possessing the smallest number of parameters. The obtained
results may appear useful at the calcuations of QQq-baryons and QQg-mesons
energy spectra.
