Aims. We report near-infrared (NIR) 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. Methods. ESO/VLT observations of the targets with the NIR spectrometer ISAAC were compared with several published NIR spectral atlases of O and B supergiants, an identification of each object's spectral characteristics was made, enabling the refinement of spectral classification of the mass donors. Results. We determined that EXO 1722-363 was of spectral type B0-B1Ia, positioned at a distance 8.0 +2.5 −2.0 kpc with a progenitor mass in the range 30-40 M . 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 stars, an intermediate evolutionary stage between massive O type stars leaving the main sequence and evolving into Wolf-Rayets. Due to the wide range in luminosity displayed by Ofpe/WNL stars, (log(L/L ) ∼ 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 × 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.