Zero modes for theD=11membrane and five-brane

There exist extremal $p$-brane solutions of $D=11\mathrm{}$ supergravity for $p=2\mathrm{} \mathrm{and} 5$. In this paper we investigate the zero modes of the membrane and the five-brane solutions as a first step toward understanding the full quantum theory of these objects. It is found that both solutions possess the correct number of normalizable zero modes dictated by supersymmetry.