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The eigenmodes of low frequency perturbations of thin anisotropic currentsheets with a finite value of the normal magnetic field, are investigated inthis paper. It is shown that two possible polarizations of symmetric andasymmetric modes (sausage and kink) exist where the growth rate ofinstabilities is positive. In addition, we demonstrate that a tearinginstability might have a positive growth rate in thin anisotropic currentsheets. The class of relatively fast wavy flapping oscillations observed byCluster is described. The main direction of wave motion coincides with thedirection of the current and the typical velocity of this motion iscomparable with the plasma drift velocity in the current sheet. Thecomparison of these characteristics with theoretical predictions of themodel of anisotropic thin current sheets, demonstrates that, in principle, thetheory adequately describes the observations

Low frequency eigenmodes of thin anisotropic current sheets and Cluster observations