Michael Cottrill and Lawrence Wnukowski from Philadelphia filed a copyright case against Spears, Zomba Recording Corp, Jive Records, Wright Entertainment Group and BMG Music Publishing.
According to Mr Cottrill and Mr Wnukowski, Spears' What U See (Is What U Get) and Can't Make You Love Me are "virtually identical" to one of their songs.
A spokesperson from Spears' record label in the UK, Jive, was unable to comment on the case on Wednesday.
The two tracks in dispute are on Spears' best-selling second album Oops! ... I Did it Again.
Rejection
Mr Cottrill and Mr Wnukowski claim that in 1999 they authored, recorded and copyrighted a song called What You See Is What You Get.
They say this song was submitted to one of Spears' representatives for consideration on a future album.
It was rejected, they say, but add that Spears' What U See (Is What U Get) and Can't Make You Love Me are based on their tune.
Last week, Mr Cottrill told the Philadelphia Daily News: "More than anything, we want the recognition that we wrote a good tune.
"We were hoping this was 'the' hit for us, a really well-done tune."
The notes for Oops! ... I Did it Again credit both songs to several writers and producers at Cheiron Studios in Sweden.
Cheiron wrote hits for the Backstreet Boys, 'N Sync and Celine Dion.
Oops! ... I Did It Again was released in May 2000, following the success of Spears' debut album Baby, One More Time from 1999.
Her third album Britney was released in 2001.