We have used reflection high-energy electron diffraction (RHEED) to study the epitaxial growth of GaAs on GaAs (001) and GaAs cut 5 ° off the (001) towards the (11̄0). Ordered arrays of steps were observed on both the singular and vicinal surfaces. The surfaces were prepared by chemically etching and then heating to 900 K to drive off the oxide. The evolution of the RHEED pattern was then followed for growth conditions given with respect to a nonequilibrium phase diagram showing the various surface reconstructions we observe for GaAs (001). Specifying growth conditions in this fashion eliminates instrumental uncertainties. The utility of RHEED for the determination of the step distribution is described and demonstrated. On the high index surface we observe an ordering of a staircase step distribution during growth. We conclude that there is an effective repulsive interaction between steps. On the singular (001) surface we observe a squarewave-like step distribution during growth that has the same periodicity as the four-fold reconstruction. When growth is halted, the squarewave distribution disapppears even though the reconstruction remains. The results are analyzed in terms of current theories that view streak formation in RHEED to be a consequence of finite domain size or thermal diffuse scattering.