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Ideal and resistive external kink-tearing-ballooning modes are studied for high-beta toroidal tokamak plasmas with a varying pedestal and/or with stabilization due to a limiter. When the pedestal value is small, the mode spectrum peaks near n=1 with a monotonically decreasing growth rate in n, in which case the most unstable mode has a structure similar to an ideal external kink mode. As the pedestal value increases, the linear growth rate decreases for a fixed beta and the mode spectrum tends to broaden. The perturbation becomes localized near the plasma edge resembling the edge relaxation phenomenon in an H-mode tokamak discharge. The stabilizing effect of a limiter on high-beta MHD modes is considered for a finite-size toroidal limiter, a poloidal limiter, and a general limiter. For the latter two types of limiters, a 3-D linear stability analysis is necessary, coupling both poloidal and toroidal modes. The high-beta toroidal case has different characteristics from the zero-beta cyclindrical case; among them is a substantial reduction in growth rate even with modest contact area. Optimum position and size of a limiter are found through extensive parameter studies. A scheme to stabilize the high-beta external kink-tearing mode by means of a set of passive feedback coils is also discussed. (ERA citation 09:027466)