Kinetic molecular beam epitaxy growth processes and the structure of the InAs (311)A surface were investigated in situ by reflection high energy electron diffraction (RHEED) and ex situ by low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). Two stable surface structures, (2X15) and (1x5), were observed by RHEED on as-grown surfaces. RHEED oscillations have a strong azimuthal anisotropy with maximum amplitude in the [(2) over bar 33] direction and minimum amplitude in the [01 (1) over bar] direction, suggesting that this surface grows via propagation and coalescence of pronounced two dimensional nuclei along the [(2) over bar 33] azimuth. Ex situ LEED and STM studies of the As-capped InAs (311)A surfaces confirmed the strong anisotropy of the surface structure. A characteristic feature of the LEED patterns is the degeneration of the principal diffraction into streaks along the [01 (1) over bar] direction. STM images show rows running along the [(2) over bar 33] direction. Although the spacing between the rows varies, there are local areas showing lateral periodicities of similar to 2.15 nm [(1X5) structure] and similar to 6.45 nm [(2X15) structure] along the [01 (1) over bar] direction, consistent with RHEED observations.