The University of Michigan said Wednesday that it was investigating whether one of its doctors had assaulted patients across several decades, becoming at least the third Big Ten university to reckon with allegations of sexual misconduct by longtime members of its medical staff.

In a statement, Michigan said that “several individuals” had described sexual misconduct by Dr. Robert E. Anderson, who worked for the university for more than 30 years and died in 2008. Although Michigan did not detail the allegations, which it said included episodes as far back as the 1970s, the university’s president, Mark Schlissel, said that the accusations were “disturbing and very serious.”

Michigan said its campus police department had opened an inquiry last summer, after Warde Manuel, the athletic director, received a message from a former student who said that Anderson had engaged in abuse during medical exams in the ’70s. During the investigation, Michigan said, other people described “sexual misconduct and unnecessary medical exams,” including at least one allegation that wrongdoing had occurred in the ’90s.

Local prosecutors decided recently that they would not bring any charges in connection to the allegations against Anderson, in part because of the state’s statute of limitations, which is generally six years.