Mass Mutual responded to the suit, saying the insurance company is not responsible for the losses of the hedge fund group, according to a report in the "Boston Globe".
But the suits allege that because the insurer benefited from the profits of Tremont in other times, it should suffer its losses as well, the newspaper reported.
Tremont suffered the second-largest loss in the Madoff scandal. Fairfield Greenwich Advisors, a New York hedge fund, lost $7.5 billion.
Lawyers argued that Tremont was acting on behalf of Mass Mutual in its investor solicitations.
In a statement about each suit obtained by the newspaper, Mass Mutual officials said, "Some of our affiliated entities are among the many victims of the illegal activities perpetrated by Bernard L. Madoff Investment Securities." Mass Mutual added that it "has strong defenses to this complaint and we will defend ourselves vigorously."