An optical photometric and proper motion study of the fields of the γ-ray bursts GRB 790613 and GRB 781124 is presented. No objects were visible on our CCD images inside the GRB 790613 error box. About 15 objects are visible on our CCD images inside the GRB 781124 error box. Two of these objects were found to be faint galaxies. Two stars with sizeable proper motions were identified near, but outside of the GRB 781124 error box. No large proper motion objects were found in the area surrounding the GRB 790613 error box.