  There are two families of non-BPS bi-spinors in the perturbative spectrum of
the nine dimensional heterotic string charged under the gauge group
$SO(16)\times SO(16)$. The relation between these perturbative non-BPS states
and certain non-perturbative non-BPS D-brane states of the dual type I$^\prime$
theory is exhibited. The relevant branes include a $\Zop_2$ charged non-BPS
D-string, and a bound state of such a D-string with a fundamental string. The
domains of stability of these states as well as their decay products in both
theories are determined and shown to agree with the duality map.
