Rail, Maritime and Transport (RMT) union drivers walked out on the Central and Waterloo and City lines in protest over the displacement of staff.
A reduced service is running on the Central Line, but there is a good service on the Waterloo and City line.
Other London Underground services are running as normal although commuters have been warned they could be busier.
The strike began at 21:00 GMT on Wednesday.
The dispute centres around plans to transfer eight train operators between Central line depots.
RMT general secretary Mick Cash said: "If [London Underground] are allowed to get away with this move on the Central Line they will start shunting drivers around at the drop of a hat regardless of the consequences."
Peter McNaught, operations director for the Central line, said: "We have made all reasonable efforts to resolve this dispute."

The cities of Gatlinburg and Pigeon Forge have suffered the worst damage.
On Thursday, country music legend Dolly Parton said her charity would donate $1,000 (Â£797) a month to families affected by the fires.
Rain on Wednesday helped quell the blaze, but officials said fires could rekindle as months of drought had left the ground extremely dry.
The wildfires, likely started by a person, spread on Monday to the tourist city of Gatlinburg. More than 14,000 residents were forced to evacuate.
Gatlinburg Fire Chief Greg Miller said: "We had trees going down everywhere, power lines - all those power lines were just like lighting a match because of the extreme drought conditions.
"So we went from nothing to over 20 plus structure fires in a matter of minutes. And that grew and that grew and that grew."
Wildfires- Why they start and how they can be stopped
Around 45 people have been treated in hospital as a result of the wildfires, and over 700 buildings have been damaged.
City mayor, Mike Werner said: "Gatlinburg is the people, that's what Gatlinburg is. It's not the buildings, it's not the stuff in the buildings.
"We're going to be back better than ever. Just be patient.''
Mr Werner has spent days reassuring his city "everything is going to be okay". Meanwhile, he has lost his home and seven other buildings he owns as part of a property business.
He said the city was still working to identify those killed by the fire.
The wildfires are also threatening Dollywood, Parton's theme park in Pigeon Forge, Sevier County.
A spokesman said guests had been evacuated from some of its properties, and that several cabins and holiday structures had been damaged.
Parton said she was "heartbroken" by the fires and that she was "praying for all the families affected by the fire - and the firefighters who are working so hard to keep everyone safe".
She said she hoped money from her charity can help to people "until they get back up on their feet".
"I know it's been a trying time for my people, and this assistance will help," she said.
"I've always believed that charity begins at home."
Singer Miley Cyrus, also a Tennessee native, sent her sympathies and support to Parton and the people of the state in an Instagram post.
Sharing a picture of the pair performing together, she wrote: "Love my fairy god mother @dollyparton and sending protective energy to the ever so sacred Dollywood and all of the homes/folks in TN who are experiencing this devastating fire!"
Twenty-six active fires have burned nearly 12,000 acres (4,855 hectares) across the state, Tennessee's Department of Agriculture reported.
Neighbouring Georgia, as well as North and South Carolina, are also battling wildfires after months of drought.
A 24-hour strike on two London Underground lines is causing disruption to commuters.
[NEXT_CONCEPT]
The death toll from wildfires across the US state of Tennessee has risen to 11 as search and rescue continues.