  We report near-infrared observations of the mass donors of the eclipsing
high-mass X-ray binary (HMXB) systems EXO 1722-363 and OAO 1657-415 in order to
derive their accurate spectral classifications. We determined that EXO 1722-363
was of spectral type B0 - B1 Ia, positioned at a distance 8.0 +2.5/-2.0 kpc
with a progenitor mass in the range 30 - 40 M_Sun. Luminosity calculations
imply that L_X ~ 10^35 - 10^37 erg s^-1 for this distance range. We conclude
that EXO 1722-363 shares many of the properties associated with other X-ray
binary B-type supergiant donors. We found that OAO 1657-415 correlates closely
with the spectra of a class of transitional objects, the Ofpe/WNL, an
intermediate evolutionary stage between massive O type stars leaving the main
sequence and evolving into Wolf-Rayets. Due to the wide range range in
Luminosity displayed by Ofpe/WNL stars, (log L/L_Sun ~ 5.3 - 6.2) distance
determinations are problematic. For OAO 1657-415 we report a distance of 4.4 <=
d <= 12 kpc, implying an X-ray luminosity of 1.5 x 10^36 <= L_X <= 10^37 erg
s^-1. We have used our new classification of OAO 1657-415 to explain the
physical processes responsible for its unique position within the Corbet
diagram. Ofpe/WNL stars demonstrate a high rate of mass-loss through a dense
stellar wind combined with a low terminal velocity. This combination of wind
properties leads to a high accretion rate and transfer of angular momentum to
the neutron star in this system. We believe this in turn leads to a smaller
instantaneous equilibrium spin period with respect to normal OB supergiants.
