Service on several of the New York area’s vital commuter rail lines was restored in time to cause only minimal headaches Monday, a day after a derailment and a crash threatened to wreak havoc at the beginning of the work week.

Still, the nation’s largest commuter railroad said that commuters should expect significant schedule changes the next few days during work to repair a track that apparently caused an empty Amtrak train to derail late Sunday.

Meanwhile, authorities investigated the cause of a PATH train crash in New Jersey on Sunday while police said it appeared that mechanical failure was to blame. More than 30 people were injured in the crash, none seriously.

Most area transit agencies honored one another’s tickets Monday, and additional buses and ferries were added to relieve some of the burden.

“I probably got here 16 minutes later than I expected to,” said Nick Guldi, arriving in the morning at Penn Station in Manhattan from Bellmore, on Long Island. “That means I won’t be able to walk to work. I’ll have to take the subway.”

Any problem along the New York-area rail network has the potential to disrupt trains that shepherd hundreds of thousands of people daily to and from the city and connect them to the subway or other regional rail systems, often through Penn Station, the nation’s busiest train depot.

Some travelers Monday were not even aware of the crash of the PATH train — short for Port Authority Trans-Hudson Corp. — a day before as it overshot the last station on its New York-to-New Jersey route and hit the bumpers at the end of the tracks.

Andrea Sanchez, 23, of New York City’s Bronx borough, read a newspaper while riding PATH into Hoboken on Monday. “I’m like, oh my God! I hope nothing happens, but it was a smooth ride.”

All three tracks were up and running at the station in Hoboken, west of Manhattan across the Hudson River, on Monday.

The Port Authority of New York and New Jersey referred questions to the National Transportation Safety Board, which is investigating. An NTSB spokesman didn’t immediately return messages.

On the east side of Manhattan, under the East River separating it from Long Island, the derailed Amtrak train caused a few commuting headaches on the extensive Long Island Rail Road.

A quarter of the trains that LIRR normally operates into Penn Station were affected, it said. More than 20 trains were canceled or diverted. The LIRR shares the affected tunnel with Amtrak.

Amtrak spokesman Cliff Cole said the train derailed because of track damage. Amtrak hopes to complete all repairs by Thursday, he said.

The LIRR said that it would operate reduced afternoon rush hour service on Monday and warned of schedule changes through Wednesday while track work proceeded.

The PATH commuter train that crashed around 8:30 Sunday morning left 34 people with mostly minor injuries and shut down the tracks for hours. Crews worked through the night to repair damage, and three tracks were back in service by Monday morning.

Officials said the train’s motorman would be tested for drugs and alcohol, standard policy in such crashes. They said there was no evidence to suggest that the motorman had been impaired at the time of the crash.

The PATH system is the main transit link between Manhattan and neighboring New Jersey urban communities and suburban commuter railroads. It handles nearly 250,000 passenger trips each weekday, fewer on weekends.

An unidentified man, who was injured during a PATH train crash at the Hoboken Terminal, is seen on a stretcher as medical officials prepare to take him to the hospital, Sunday, May 8, 2011, in Hoboken, N.J. A spokesman says a train pulling into the station struck an abutment, causing minor injuries. (AP Photo/Julio Cortez)