  We consider two inequivalent truncations of the super D9--brane: the
``Heterotic'' and the ``Type I'' truncation. Both of them lead to an N=1
nonlinear supersymmetrization of the D=10 cosmological constant. The
propagating degrees of freedom in the Heterotic and Type I truncation are given
by the components of a D=10 vector multiplet and a single Majorana-Weyl spinor,
respectively. As a by-product we find that, after the Type I truncation, the
Ramond-Ramond super ten-form provides an interesting reformulation of the
Volkov-Akulov action. These results can be extended to all dimensions in which
spacetime filling D-branes exist, i.e. D=3,4,6 and 10.
