Busted had eight top 10 hits between 2002 and 2004
Ki McPhail and Owen Doyle say they wrote songs with James Bourne and Matt Willis when the group formed in 2001.
But they claim they were forced to sign away their rights after "threats" and "undue pressure" when they were sacked from the band later that year.
The songs include Year 3000 and What I Go To School For, which went on to be huge hits for the now-defunct group.
Mr McPhail and Mr Doyle were in a band called The Termites with Mr Bourne and Mr Willis between January and October 2001, the High Court in London heard.
'In the dark'
They also wrote songs including Sleeping with the Light On and Psycho Girl together during that time, the claimants said.
That March, the four signed a deal with a professional management company, changing their name to Busted the following month.
In October, however, Mr McPhail and Mr Doyle say they were kicked out of the group and coerced into signing an agreement that released their claim to the group's material.
The pair said they were not told record label Universal liked the songs and had offered Busted a lucrative record deal when they signed the agreement.
They are now seeking to set aside that agreement on the basis of undue influence and misrepresentation.
Tim Penny, representing the pair, said: "The pressure placed on the claimants consisted of repeated advice and threats.
He said they were told "unless they released their claims in relation to the group members' songs and in particular the four songs, they would be sued, Ki McPhail's parents would lose their home and the claimants would never work in the industry again".
Singer Charlie Simpson subsequently joined the group, remaining with them until they split up in 2005.The case continues at the High Court before Mr Justice Morgan. The hearing is expected to last 15 days.