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An additional spheroidal integral of motion and a group of dynamic symmetryin a model quantum-mechanical problem of two centres eZ_{1}Z_{2}omega withCoulomb and oscillator interactions is obtained, the group properties of itssolutions being studied. P(3) \otimes P(2,1), P(5,1) and P(4,2) groups areconsidered as the dynamic symmetry groups of the problem, among them P(3)\otimes P(2,1) group possessing the smallest number of parameters. The obtainedresults may appear useful at the calcuations of QQq-baryons and QQg-mesonsenergy spectra.Comment: 15 pages, LaTe

Non-geometrical symmetry and separation of variables in the two-centre problem with a confinement-type potential