Supermembranes and eleven-dimensional supergravity

We construct an action for a supermembrane propagating in d=11 supergravity background. Using the constraints of d=11 curved superspace, we show that the action is invariant under Siegel-type transformations recently generalized by Hughes, Li and Polchinski. The transformation parameter is a world-volume scalar and d=11 spacetime spinor. We also discuss the general problem of the coupling of n-dimensional extended objects to d-dimensional supergravity.