The two surviving members of the Beatles are using EMI and Capitol Records, claiming they conned the band out of millions of dollars.
Sir Paul McCartney, Ringo Starr and relations of George Harrison and John Lennon are seeking at $25m (£13.2m) in damages.
Last week, a New York State Supreme Court judge denied EMI's request for the claim to be thrown out.
The Beatles are also seeking to reclaim rights to all their master recordings. The band say EMI and Capitol wrongly classified copies of Beatles recordings as destroyed, but then secretly sold them.
They also claim the number of units sold was under-reported, and the firms classified some recordings as "promotional" and as a result non-royalty bearing, but then sold the material.
"We are delighted to have the opportunity to pursue this claim for the return of the Beatles' master recordings," the Beatles’ lawyer says.