We present a systematic study of the morphology of homoepitaxial InP films grown by metalorganic vapor-phase epitaxy which are imaged with ex situ atomic force microscopy. These films show a dramatic range of different surface morphologies as a function of the growth conditions and substrate (growth temperature, V/III ratio, and miscut angle <0.6∘ and orientation toward A or B sites), ranging from stable step flow to previously unreported strong step bunching, over 10 nm in height. These observations suggest a window of growth parameters for optimal quality epitaxial layers. We also present a theoretical model for these growth modes that takes account of deposition, diffusion, and dissociation of molecular precursors, and the diffusion and step incorporation of atoms released by the precursors. The experimental conditions for step flow and step bunching are reproduced by this model, with the step bunching instability caused by the difference in molecular dissociation from above and below step edges, as was discussed previously for GaAs (001).