The University of Southern California was hit with multiple lawsuits on Monday — claiming it failed to address complaints about a campus gynecologist who was allegedly preying on female students “for decades.”

The suits contain disturbing new allegations of sexual abuse and molestation against Dr. George Tyndall, who was accused last week of harassment and racial discrimination.

They include claims that he once inserted his “entire ungloved fist” inside a woman while making “vulgar and demeaning” statements about her genitalia — and numerous other instances of “unwanted sexual touching.”

During one exam, Tyndall allegedly “violated” a first-year graduate student while a female nurse aka “chaperone” was waiting outside. He later claimed that the student, Lucy Chi, had “given him permission to proceed” — “as if the violation of protocol and standard of care was Chi’s fault,” according to court documents obtained by The Post.

Chi is suing USC, its board of trustees and Tyndall as part of a class-action lawsuit filed Monday in the US District Court for the Central District of California. Five other women filed civil lawsuits in Los Angeles County Superior Court.

Attorneys from the consumer-rights class-action law firm Hagens Berman plan to represent Chi and “a proposed class of hundreds, if not thousands, of female students” who received a medical examination from Tyndall and were allegedly subjected to his “creepy behavior.”

In their complaint, they accuse USC of covering up the doc’s debauchery “for decades” and violating its female students’ trust “by knowingly putting women in the room for treatment” by him.

“In fact, USC nurses, chaperones and other staff members were regularly present in the examination rooms, observed the inappropriate sexual molestation, and took no steps to stop it as it occurred,” the complaint says.

Chi claims to have been inappropriately touched by Tyndall in 2012 during her annual exam at USC’s student health center. The longtime gynecologist “penetrated her with his fingers” and “told her that he wanted to check whether the speculum would fit,” the complaint says.

He then allegedly conducted a breast exam with his bare hands, and no sheet covering — so that he could see her entire upper body “at the same time.”

During the exam, Tyndall “squeezed” Chi’s breasts and fondled her in “an atypical way,” the complaint says, alleging that Chi felt “violated and embarrassed.”

“She did not go back to him,” it adds.

The other lawsuits that were filed Monday against USC and Tyndall contain similar accusations from five former students. Four of the women are suing as a group and the fifth has reportedly filed her own suit.

The group is being represented by Orange County lawyer John Manly — who helped secure the $500-million Larry Nassar settlement from Michigan State University last week.

“This action seeks to vindicate the rights of four young women who were sexually abused, harassed and molested at the hands of serial sexual predator,” their complaint says. “While attending Defendant USC, Plaintiffs were forced to repeatedly seek medical treatment from Tyndall, due to the fact that he was the only full-time gynecologist on staff at Defendant USC’s Student Health Clinic.”

According to the group, Tyndall “used this position of trust and authority to sexually abuse Plaintiffs on multiple occasions, by engaging in acts that include but are not limited to: forcing Plaintiffs to strip naked, groping Plaintiffs’ breasts, digitally penetrating Plaintiffs’ vaginas, and spread open their anal crevice so he could leer at the crevice and anus, for no legitimate medical purpose and for no other reason than to satisfy his own prurient sexual desires.”

Tyndall also allegedly behaved this way when examining the fifth woman.

She claims in her suit that he commented on the tightness of her genital muscles while inserting his fingers inside her.

“She’s in hindsight thinking, ‘I’m not sure there’s a reason for that to be done,'” the woman’s attorney, David Ring, told the Los Angeles Times.

In each case, the lawyers plan to argue that the two-year statute of limitations does not apply to Tyndall because his alleged victims had no idea that they were being preyed upon.

“For 99.95% of these patients, they didn’t have a true understanding of the abuse until last week,” explained Ronald Labriola, an Irvine lawyer who is aiding Manly with the suit.

Tyndall’s alleged conduct was first revealed in a pair of LA Times stories last week, which featured interviews from more than a dozen former students. Several of the women suing USC say they didn’t know they were abused until after seeing what the others told the Times.

“Chi read the articles that disclosed Tyndall’s wrongdoing [and] became extremely upset and angry that USC let Tyndall violate her and others over such a long period of time,” her complaint says. “She felt distressed all over again, replaying Tyndall’s violation of her in her mind.”

At the time of the alleged incident, Chi was “not sure” about what had happened — and “did not feel like she was in a position to second guess the doctor,” according to her complaint.

But she eventually found the courage to come forward.

“For decades, USC has silenced the women who were violated in unspeakable ways by Dr. Tyndall, willfully ignoring the alarming complaints from nurses and patients as more and more students were sent into his office,” said Steve Berman, managing partner of Hagens Berman, the firm representing Chi. “Our plaintiff and other women have bravely stepped forward to report these heinous acts, and through this lawsuit, we intend to hold defendants accountable.”

The suits filed Monday bring various charges against Tyndall, USC and its board of trustees — including violations of Title IX, violation of the California Equity in Higher Education Act, gender violence, gross negligence, civil battery and intentional infliction of emotional distress.

In response, USC sent The Post a statement saying: “We are aware of the lawsuits. We are focused on ensuring the safety and well-being of our students and providing support to those affected.”

School officials have urged anyone with additional information or allegations to contact the university or student health center.

USC’s provost, Michael Quick, issued a letter Monday apologizing to Tyndall’s patients — while also defending top administrators and their handling of his complaints.

“I have seen media reports allege, that the university leadership knew about Dr. Tyndall’s misbehavior for a long time, and that we covered it up for the sake of the USC brand. This is absolutely untrue,” explained Quick, calling it “unthinkable.”

“It is true that our system failed, but it is important that you know that this claim of a cover-up is patently false,” he said. “We would never knowingly put students in harm’s way.”

Tyndall has denied any wrongdoing, saying his exams were appropriate and “extremely thorough.” He could not be reached for comment Monday.