  The standard eleven-dimensional supergravity action depends on a three-form
gauge field and does not allow direct coupling to five-branes. Using previously
developed methods, we construct a covariant eleven-dimensional supergravity
action depending on a three-form and six-form gauge field in a
duality-symmetric manner. This action is coupled to both the M-theory two-brane
and five-brane, and corresponding equations of motion are obtained. Consistent
coupling relates D=11 duality properties with self-duality properties of the
M-5-brane. From this duality-symmetric formulation, one can derive an action
describing coupling of the M-branes to standard D=11 supergravity.
