Open branes ending on other branes, which may be referred to as the ho
st branes, are studied in the superembedding formalism. The open brane
, host brane and the target space in which they are both embedded are
all taken to be supermanifolds. It is shown that the superspace constr
aints satisfied by the open brane are sufficient to determine the corr
esponding superspace constraints for the host branes, whose dynamics a
re determined by these constraints. As a byproduct, one also obtains i
nformation about the boundary of the open brane propagating in the hos
t brane. (C) 1998 Published by Elsevier Science B.V. All rights reserv
ed.