The microscopic surface features were observed during the molecular-beam epitaxy of InxGa1-xAs on InP (100) substrates by scanning microprobe reflection high-energy diffraction in real time as a function of x from 0.41 to 0.96. In the case of In0.41Ga0.59As (the lattice mismatch of the strained layer was f = -0.77%, where the minus sign represents a smaller lattice constant of an epitaxial layer than that of a substrate), three-dimensional island growth was observed from the start of growth. On the other hand, two-dimensional layer-by-layer growth was maintained during growth of InxGa1-xAs with x = 0.45-0.75 (f = -0.47 to +1.48%, where the plus sign represents a larger lattice constant of an epilayer than that of a substrate). While the growth of compressive epilayers with f between +0.36% and +1.48% proceeded, a surface crosshatched morphology was observed after the growth of certain film thicknesses, which were dependent on the lattice mismatch. A rough textured morphology was observed instead of a crosshatched morphology for those epilayers with a lattice mismatch greater than +2.29% (In0.87Ga0.13As), where three-dimensional island growth was favored over the layer-by-layer growth mode. Transmission electron microscope observations showed that the presence of a surface crosshatched pattern was correlated with the presence of 60-degrees mixed misfit dislocations. The result indicates that the thickness at which the crosshatched line appears represents the critical layer thickness corresponding to misfit dislocation generation.