Serial sex offenders are a big problem on subways, should they be banned for life?

The officers follow them through jam-packed platforms and onto crowded trains, waiting to see if they grope, grind, molest or indecently expose themselves again.

Because only then can police intervene and make an arrest or eject them from the subway system.

Authorities have long been frustrated by not being able to keep known subway sexual harassers from returning to the scene of their crimes.

But now, lawmakers and police officials are pushing a dramatic measure: On Monday, a city councilman, Chaim Deutsch, introduced a bill that would bar repeat sexual offenders from the subway system for life.

Gov. Andrew Cuomo and Mayor Bill de Blasio endorsed the idea of dealing more forcefully with sexual predators, though they stopped short of embracing a lifetime ban.

“If someone shoplifts in a store, and they are a recidivist, then that person could be banned from walking into the store,” said Deutsch, who represents parts of Brooklyn.

“This should not be any different,” added Deutsch, who said he was prompted to pursue the bill by an article in The New York Post about the challenges the police face in thwarting repeat subway sexual offenses.

City Council members often introduce bills that do not progress very far and Deutsch’s bill likely faces long odds.

Still, it has prompted a debate about a problem that many women who ride the subway must contend with on a near-daily basis.

“We have individuals who, literally, since the 1980s have been committing sexual offenses on the trains,” the Police Department’s chief of detectives, Dermot F. Shea, said Wednesday during a news conference in Brooklyn. Shea spoke outside the Brooklyn Bridge-City Hall subway station, where police said they had earlier that day arrested a man for forcibly touching a 15-year-old girl.

Cuomo, who controls the subway, said he supported barring sexual offenders after a second conviction.

“This is one of these issues that I think common sense needs to prevail,” he told reporters in Albany on Tuesday, adding that groping and grinding was “a major problem.”

A precedent for such measures, the governor said, already existed because of laws that prohibit sexual offenders released from prison from living near schools.

“You have people who target people in the subways,” he said, adding that the high recidivism rate for such crimes shows that existing laws were ineffective. “Why keep doing the same thing over and over and over again?”

De Blasio also did not say specifically whether he supported Deutsch’s bill, but said he would support legislation that would “help us do more to go at these predators and get them off the subway.”

The Metropolitan Transportation Authority, which runs the subway, issued a statement saying that it supported efforts to keep repeat sexual offenders out of the subway.

The number of sex crimes, including felonies and misdemeanors, on the subway are on the rise — 165 were reported through March 17, a 10 percent increase compared with the same period last year, according to the New York Police Department.

Even though victims of sexual offenses have been encouraged to come forward for years, Shea said he still believed the number of crimes did not reflect the extent of the problem.

In recent years, police and the transit agency have focused on making victims more willing to report criminal encounters.

As part of that campaign, the Police Department has trained more female officers to work on sex-crime cases in the subway. They have also encouraged riders to submit cellphone camera photos and videos that could help them identify suspects and have posted these photos on social media.

Still, because most sexual offenses committed on the subway are misdemeanors, prosecutors are limited in punishing convicted offenders and keeping them out of the subway, said Chief Edward Delatorre, who oversees the Police Department’s transit bureau.

In Albany, state Sen. Diane J. Savino, a Democrat who represents Staten Island and Brooklyn, has been working for several years to increase the penalties for people who repeatedly commit sexual offenses on the subway.

“Right now, these offenders are only committing misdemeanors and can only be sentenced to up to a year in jail, with most serving little to no time at all,” Savino said.

While Savino said she supported the ban proposed by Deutsch, she believed it would be hard to enforce.

“They can’t be expected to have people at every turnstile checking who gets on and off the subway,” she said. “The real solution is to properly punish these crimes.”

A bill she has sponsored would make unwanted sexual contact on public transportation — what Savino called “subway grinding” — a felony. The bill was passed by the Senate three times between 2013 and 2018, all while the chamber was controlled by Republicans, but never made it past the in Democratic-controlled Assembly’s Committee on Codes, which has jurisdiction over criminal justice policy.

“Their attitude is that these penalties are severe enough,” she said of committee. “But they’re not. If they were, you would not have repeat incidents by the same predators.”

This article originally appeared in The New York Times.