AbstractThe nonlinear evolution of external ideal MHD-modes is determined from the equations of ideal MHD by employing a reductive perturbation method which uses a driving parameter for expansion. The reduction of the plasma equations is the same as for internal modes and was treated previously [1]. A main problem arising in addition for external modes is the reduction of the nonlinear boundary conditions. The set of reduced boundary conditions is obtained on the undisplaced boundary in the marginally stable equilibrium position. Another additional problem arises from the fact that the linear MHD operator is only selfadjoint for linear eigenmodes but not for the higher order mode corrections. This complicates the determination of nonlinear amplitude equations for the marginal mode which are obtained from solubility conditions. The amplitude equations are qualitatively the same as for internal modes. Quantitatively, the calculation of the coefficients in these is different. Explicit expressions for the coefficients are derived in full generality. The effect of higher order corrections to the nonlinear amplitude equations is discussed quantitatively for one of two possible cases and qualitatively for the other.