The deposition of lattice mismatched InAs on (0 0 1)InP by gas source molecular beam epitaxy leads to the formation of quantum sires in contrast to the familiar dot formation in the InAs/GaAs system. The paper describes two processes: (i) the formation of a two-dimensional, alloyed layer InAsyP1-y in a pre-deposition phase and (ii) the strain relaxation process into wire-like structures, when depositing InAs on top. The quantum wires have been investigated using atomic force microscopy, transmission electron microscopy, and transport anisotropy measurements.