The interaction of gallium with single crystalline copper surfaces has been investigated by means of high energy glancing angle electron diffraction, transmission microscopy and metallography. Surface structural changes and morphological changes were both recorded. Gallium was deposited in-situ onto both bulk single crystalline copper surfaces and thin film Cu surfaces grown in-situ on (100) NaCl surface inside the HEED apparatus.Cu-Ga alloy films were observed to grow epitaxially at room temperature on clean (111), (001) and (110) copper surfaces. The epitaxial growth was obgerved only with a deposition rate for Ga of approximately 30 A/min. and on clean copper surfaces. No epitaxial growth of Cu-Ga alloy films was observed on surfaces covered with cuprous oxide. Higher deposition rates always gave diffuse ring type patterns. An early stage ordered ʓ h.c.p. phase was observed to grow on Cu (111) face. A later stage Ø tetragonal phase was observed to grow on all three faces of Cu with three orientations on the (111) face, four major orientations on the (001) face and two orientations on the (110) face.