Multilayer epitaxial structures consisting of InxGa1-xAs layers of various compositions were grown on GaAs substrates by the molecular beam epitaxy technique. Dislocation evolution and residual strain in these heterostructures were studied using cross-sectional transmission electron microscopy (XTEM) and high-resolution x-ray diffraction analyses, respectively. The multilayer heterostructures were designed such that the compositional difference between two adjacent InxGa1-xAs layers in the stack was less than a critical compositional difference of DELTA-x = 0.18, taking partial lattice-relaxation into account. XTEM studies of the stacked structures indicated dislocation evolution to be confined to the GaAs substrate and the InxGa1-xAs layers underlying the top InxGa1-xAs layer in the stack, the top InxGa1-xAs layer being essentially dislocation-free. This phenomenon is attributed to a monotonic increase in the yield strength of InxGa1-xAs at the appropriate growth temperatures with increasing values of x. Such behavior appears to persist up to an InGa1-xAs composition of approximately x = 0.5, whereupon a further increase in composition results in dislocation evolution in the top layer of the stack. It is postulated that the yield strength of InxGa1-xAs decreases with increasing values of x beyond x = 0.5. Extremely low dislocation density InxGa1-xAs material was grown on GaAs using the stacked structure approach as evidenced by etch pit analysis. For example, dislocation densities of 1-2 X 10(3)/cm2 and 5-6 X 10(3)/cm2 were recorded from In0.35Ga0.65As and In0.48Ga0.52As top layers, respectively. Such InxGa1-xAs alloys would be potentially suitable for the fabrication of photonic devices operating at 1.3-mu-m (x = 0.35) and 1.55-mu-m (x = 0.48).