The relation between some perturbative non-BPS states of the heterotic theo
ry on T-4 and non-perturbative non-BPS states of the orbifold limit of type
IIA on K3 is exhibited. The relevant states include a non-BPS D-string, an
d a non-BPS bound state of BPS D-particles ('D-molecule'). The domains of s
tability of these states in the two theories are determined and compared.