In the 1960s and 70s, Maxwell served as WHOI Director of Research and Provost, working closely with WHOI President Paul Fye and helping to found the MIT-WHOI Joint Program in Oceanography. During his time at the Institution, Maxwell also pursued his own research in geophysics. Among other achievements, he was appointed President of the American Geophysical Union (1976-1978) and co-led an expedition of the Deep-Sea Drilling Project, which provided critical evidence to support the theory of plate tectonics by demonstrating that the seafloor under the South Atlantic was spreading.