Atomic ordering in InGaAs, InAlAs, and GaAsSb crystals grown on (110) InP substrates by molecular beam epitaxy, has been studied by transmission electron microscopy. In the electron diffraction pattern from these crystals, superstructure spots associated with CuAu-I type ordered structure are found. When the tilting angle of the substrates increases, the ordering becomes stronger. The ordering is also stronger in crystals grown on substrates tilted toward the <001> or the <001> direction than those on substrates tilted toward the <110> direction. From these results, one can conclude that atomic steps on the growth surface play an important role in the formation of ordered structures. The ordering becomes stronger when the growth temperature increases. In high resolution images of the crystal, doubling in periodicity of 220 and 200 lattice fringes is found, which is associated with CuAu-I type ordered structure. Moreover, anti-phase boundaries are very often observed in the ordered regions. It is also found that ordering is not perfect, and that ordered regions are plate-like microdomains lying on planes slightly tilted from the (110) plane. On the basis of these results together with considerations of the atomic arrangement of the ordered structure and surface reconstruction on the (110) plane, we propose four possible models for the ordering. Through precise evaluation of these models, two models are selected as the most probable ones: these involve formation of the ordered structures on surfaces dominated by two monolayer steps. These models have been experimentally proven by the analyses of electron diffraction patterns from different InGaAs crystals grown on different growth surfaces. We have fabricated InGaAs/N-InAlAs heterostructures with a strongly ordered InGaAs channel layer. The measured two-dimensional electron gas mobilities from these structures are found to be 100,000 cm2/Vs in the <110> direction and 161,000 cm2/Vs in the <110> direction with a sheet electron concentration (Ns) of 9.5 × 1011 cm−2 at 6 K. The latter mobility is much higher than both calculated alloy scattering limited mobility and the best experimental results for lattice-matched InGaAs/N-InA]As systems. The mobility enhancement in the <110> direction is considered to be achieved by the suppression of alloy scattering due to the occurrence of ordering in the InGaAs channel layer.