We report experiments in which we attempted to grow Ge and Si0.2Ge0.8 films with a tetragonal crystal structure on InP(001). The substrate was chosen because it has approximately the same lattice constant as the tetragonal SixGe1-x a-axis lattice constant. The tetragonal structure has been observed previously in Ge, and has a 1.5-eV bandgap. Theory predicts that the gap is direct, which implies that tetragonal SixGe1-x films are suitable for optoelectronic devices. Growth on the InP(001) (2 X 3) and (2 X 4) reconstructed surfaces was investigated. Some evidence for the tetragonal phase was obtained for the growth of Si0.2Ge0.8 at 100 degreesC on the two reconstructions, but no evidence was obtained for growth of either tetragonal Si0.2Ge0.8 or Ge on the (2 X 3) reconstruction for growth temperatures at or above 130 degreesC. We conclude that tetragonal SixGe1-x films on InP(001) does not seem to be a technologically feasible material system.