Duality between the E-8 x E-8 heterotic string and Type I' theory pred
icts a tower of D(irichlet)-particle bound states corresponding to per
turbative heterotic string states. In the limit of infinite Type I' co
upling, some of these bound states become massless, giving rise to enh
anced E-8 x E-8 gauge symmetry. By taking a different infinite couplin
g limit, one can recover the E-8 x E-8 gauge bosons of M-theory, compa
ctified on S-1/Z(2). In this paper we use the matrix model description
of the D-particle dynamics to study these bound states. We find resul
ts consistent with the chain of dualities and clarify a number of issu
es that arise in the application of the matrix mechanics to this syste
m. (C) 1997 Elsevier Science B.V.