Abstract (Elsevier)
We construct an action for a supermembrane propagating in d = 1 supergravity background. Using the constraints of d = 11 curved superspace, we show that the action is invariant under Siegel-type tranformations 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.