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 four or eight supersymmetries) by dualizing 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 eight supersymmetries, the linear multiplet is off-shell in contrast to the scalar multiplet. The dynamics of the L-branes 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.
