CuAu-I type ordered structures in InGaAs grown on (110) InP substrates by molecular beam epitaxy, have been studied by transmission electron microscopy. In the electron diffraction pattern from the InGaAs, superstructure spots associated withCuAu-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 the range 360-485°C. In high resolution images of the crystal, doubling in periodicity of 220 and 200lattice 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.