Eigenmodes of Coherent Oscillations in Colliding Beams. Coherent oscillations in colliding non-rigid bunches are studied on the basis of the Vlasov equation. Tuneshifts of uncoupled modes, the beam-beam contribution to mode coupling and the Landau damping due to the incoherent beam-beam tunespread are considered. The influnce on the TMCI of the beam-beam interaction in the presence of both a finite crossing angle and an offset at the collision point is discussed.