The evolution of surface roughness in epitaxial Si0.7Ge0.3alloys grown on Si(001) as a function of temperature (200–600 °C), thickness (t=7.5–100 nm), and substrate miscut were investigated by atomic force microscopy and quantified in terms of the height‐difference correlation functionG(&rgr;), in which &rgr; is lateral distance and [G(&rgr;→∞)]1/2is proportional to the surface width. The films were deposited by ultrahigh vacuum ion‐beam sputter deposition at 0.1 nm s−1. Strain‐induced surface roughening was found to dominate in alloys grown on singular Si(001) substrates atTs≳450 °C where [G(&rgr;→∞)]1/2initially increases with increasingtthrough the formation of coherent islanding. The islands are preferentially bounded along ⟨100⟩ directions and exhibit 105 faceting. This tendency is enhanced, with much better developed ⟨100⟩ islands separated by deep trenches—of interest for growth of self‐assembled nanostructures—in films grown on Si(001)‐4°[100]. Increasing the film thickness above critical values for strain relaxation leads to island coalescence and surface smoothening. At very low growth temperatures (Ts≤250 °C), film surfaces roughen kinetically, due to limited adatom diffusivity, but at far lower rates than in the higher‐temperature strain‐induced regime. Si0.7Ge0.3alloy surfaces are smoother, while the films exhibit larger critical epitaxial thicknesses, than those of pure Si films grown in this temperature regime. There is an intermediate growth temperature range, however, over which the alloy film surfaces remain extremely smooth even at thicknesses near critical values for strain relaxation. This latter result is of potential importance for device fabrication. ©1996 American Institute of Physics.