We obtain the Hamiltonian form of the world-volume action for the M5-b
rane in a general D = 11 supergravity background, We use this result t
o obtain a new version of the covariant M5-brane Lagrangian in which t
he tension appears as a dynamical variable, although this Lagrangian h
as some unsatisfactory features which we trace to peculiarities of the
null limit. We also show that the M5-brane action is invariant under
all (super)isometries of the background. (C) 1998 Elsevier Science B.V
.