An analysis of supersymmetric Kaluza–Klein theories is begun by obtaining the Casimir operators for the super‐Poincaré algebra in any number of dimensions. The knowledge of these operators is used to decompose the general scalar superfield in 11 dimensions into its irreducible parts. The irreducible superfields are expressed as products of Grassmann–Hermite functions and Grassmann–Bargmann–Wigner multispinor fields. Some Lagrangians for these superfields are written down. The formulation is off shell but global.