We use normal coordinate methods to obtain the expansion with respect to fe
rmionic coordinates of the 11-dimensional supermembrane action in a supergr
avity background. Likewise, expansions for various branes in other dimensio
ns can be obtained. These methods allow a systematic and unambiguous expans
ion of the vielbein to any order in the fermionic coordinates and avoid the
complications encountered in the gauge completion approach. (C) 2001 Publi
shed by Elsevier Science B.V.