We study the dynamics of D-particles (D0-branes) in type I' string the
ory and of the corresponding states in the dual heterotic description.
We account for the presence of the two eight-orientifolds (eight-dime
nsional orientifold planes) and sixteen D8-branes by deriving the appr
opriate quantum mechanical system. We recover the familiar condition o
f eight D8-branes for each eight-orientifold. We investigate bound sta
tes and compute the phase shifts for the scattering of such states and
find that they agree with the expectations from the supergravity acti
on. In the type I' regime we study the motion transverse to the eight-
orientifold and find an interesting cancellation effect.