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We perform variable separation in the quasi-potential systems of equations ofthe form $\ddot{q}=-A^{-1}\nabla k=-\tilde{A}^{-1}\nabla\tilde{k}${}, where $A$and $\tilde{A}$ are Killing tensors, by embedding these systems into abi-Hamiltonian chain and by calculating the corresponding Darboux-Nijenhuiscoordinates on the symplectic leaves of one of the Hamiltonian structures ofthe system. We also present examples of the corresponding separationcoordinates in two and three dimensions.Comment: LaTex, 30 pages, to appear in J. Phys. A: Math. Ge

Separation of variables in quasi-potential systems of bi-cofactor form