  We investigate the effective worldvolume theories of branes in a background
given by (the bosonic sector of) 10-dimensional massive IIA supergravity
(``massive branes'') and their M-theoretic origin. In the case of the solitonic
5-brane of type IIA superstring theory the construction of the Wess-Zumino term
in the worldvolume action requires a dualization of the massive
Neveu-Schwarz/Neveu-Schwarz target space 2-form field. We find that, in
general, the effective worldvolume theory of massive branes contains new
worldvolume fields that are absent in the massless case, i.e. when the mass
parameter m of massive IIA supergravity is set to zero. We show how these new
worldvolume fields can be introduced in a systematic way. In particular, we
find new couplings between the massive solitonic 5-brane and the target space
background, involving an additional worldvolume 1-form and 6-form. These new
couplings have implications for the anomalous creation of branes. In
particular, when a massive solitonic 5-brane passes through a D8-brane a
stretched D6-brane is created. Similarly, in M-theory we find that when an
M5-brane passes through an M9-brane a stretched Kaluza-Klein monopole is
created. Pairs of massive branes of type IIA string theory can be viewed as the
direct and double dimensional reduction of a single ``massive M-brane'' whose
worldvolume theory is described by a gauged sigma model.
