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."
A 24-hour strike on two London Underground lines is causing disruption to commuters.