Actions for branes, with or without worldsurface gauge fields, are discussed in a unified framework. A simple algorithm is given for constructing the component Green-Schwarz actions. Superspace actions are also discussed. Three examples are given to illustrate the general procedure: the membrane in D = 11 and the D2-brane, which both have on-shell worldsurface supermultiplets, and the membrane in D = 4, which has an off-shell multiplet.

The superembedding approach to p-branes is used to study a class of p-branes which have linear multiplets on the worldvolume. We refer to these branes as L-branes. Although linear multiplets are related to scalar multiplets (with 4 or 8 supersymmetries) by dualising one of the scalars of the latter to a p-form field strength, in many geometrical situations it is the linear multiplet version which arises naturally. Furthermore, in the case of 8 supersymmetries, the linear multiplet is off-shell in contrast to the scalar multiplet. The dynamics of an L-brane are obtained by using a systematic procedure for constructing the Green-Schwarz action from the superembedding formalism. This action has a Dirac-Born-Infeld type structure for the p-form. In addition, a set of equations of motion is postulated directly in superspace, and is shown to agree with the Green-Schwarz equations of motion. †