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We continue the study of the existence and stability of static sphericalmembrane configurations in curved spacetimes. We first consider higher ordermembranes described by a Lagrangian which, besides the Dirac term, includes aterm proportional to the scalar curvature of the world--volume ${}^{(3)}R$.Notably, in this case, the equations of motion can be reduced to second orderones and an effective potential analysis can be made. The conditions forstability are then explicitly derived. We find a self--consistent staticspherical membrane, determining the spacetime generated by the membrane itself.In this case we find, however, that the total energy of the membrane has to benegative, and no {\it stable} equilibrium can be achieved. We then generalizethe discussion to a membrane described by a Lagrangian including all possiblesecond derivative terms. We conclude the paper with some discussion on thegenerality of the results obtained.Comment: 11 pages, REVTE

Are higher order membranes stable in black hole spacetimes?