We have grown ferromagnetic alpha-MnAs layers on GaAs(001) by molecular beam epitaxy. The surface was studied during growth by reflection high-energy electron diffraction (RHEED) and reflectance difference spectroscopy (RDS) and after growth by in situ scanning tunneling microscopy (STM). During nucleation on the c(4x4) reconstructed GaAs(001) surface the RHEED pattern disappears. STM images at this stage show well defined steps and flat terraces, but a disordered structure on the terraces. After deposition of 1.5 ML MnAs small three-dimensional clusters have been observed by STM. For thicker layers several phases of the MnAs((1) over bar 100) surface with different reconstructions have been observed by RHEED. Intensity oscillations of the specular spot have been found for As-rich growth at 265 degrees C substrate temperature and deposition rates of 0.2-0.65 ML/s. For temperatures below 360 degrees C a feature was found in the RD spectra that is sensitive to the surface reconstruction. At higher temperatures the RD spectra did not depend on the surface structure. The (1x2) and (1x1) reconstructions have been cooled down to room temperature. Atomic scale images of these surfaces an presented. The images of the (1x2) structure show asymmetric protrusions, consequently this structure has only onefold symmetry. This leads to the formation of reconstruction domains with opposite orientations of the unit mesh in adjacent domains. The domain boundaries run along the [0001] direction.