By Milton J. Valencia and Martin Finucane Globe Staff

Federal prosecutors have recommended that Catherine Greig, the girlfriend of James “Whitey” Bulger, serve 10 years in federal prison for helping the notorious gangster remain a fugitive for 16 years.

The prosecutors have also asked that Greig, 61, pay a $150,000 fine and serve three years of supervised release.

She is slated to be sentenced Tuesday in US District Court in Boston.

“This is no garden variety harboring case,” First Assistant US Attorney Jack W. Pirozzolo said in court documents filed Friday. “It is the most extreme case of harboring this district has seen For over 16 years, Greig conspired to, and did, protect Bulger – alleged to be one of the most dangerous and violent criminals in the history of this district – from being discovered by law enforcement.”

Greig has been held without bail since she and Bulger were arrested on June 22, 2011, outside their Santa Monica, Calif., apartment.

She pleaded guilty in March to harboring Bulger, conspiracy to commit identity fraud, and identity fraud. She faces up to five years in prison and a $250,000 fine for each charge.

During the time Bulger and Greig spent in Santa Monica -- from at least 1996 to the time of their arrests -- Greig “handled money for Bulger, dealt with his medical providers, lied on multiple occasions about her own identity when she herself was seeking medical care, and was the key actor in the conspiracy to protect Bulger from being discovered,” the prosecutor said in a filing recommending the sentence.

Among the revelations in the filing: Bulger told law enforcement authorities that he and Greig had both been aware of the public service announcements that the FBI had released in June 2011 that had focused on Greig.

Bulger, with what turned out to be prescience, told Greig, “This is it,” according to the filing.