It is the latest legal row to erupt since the project was completed in 2011 at a cost of £152m.
A council spokesperson said: “We have lodged a formal claim with the court and are proceeding with legal action against BAM Nuttall. The claim is for the cost to repair defects on the Guided Busway.
“This follows a thorough review and advice from external legal and technical experts, who have assessed the work and the contract.
“BAM Nuttall are defending the claim and if this continues the claim will have to be heard by the courts and a potential trial is unlikely to be until the end of 2021 or possibly 2022.
“It would be inappropriate to comment further while legal proceedings are active.”
An initial legal dispute over cost overruns and late delivery of the project saw BAM Nuttall pay the county council £33m in an out-of-court settlement in 2013 to cover defects and extra work.
Since then the council claims further defects have appeared in the busway infrastructure.
A spokesperson for BAM Nuttall said: “Since the busway opened in 2011 passenger numbers have grown 47 per cent. The busway is a fantastic piece of transport infrastructure which has performed consistently and reliably.
“In the six years since the council’s consultants alleged that the busway would need hundreds of interventions each month, this has not come to pass. The engineering evidence shows that it will not come to pass in the future.
“BAM has long sought to work with the council to address its concerns. We’ve assured the council, on many occasions, that anything wrong with the busway design, for which BAM Nuttall is responsible, we’ll put it right
“It’s disappointing that the council is progressing the matter through litigation in the High Court. Our next step is to explore the details of Cambridgeshire County Council’s claim.
“BAM is confident that we’ll demonstrate, to the satisfaction of the court that the design of the busway is not fundamentally defective and doesn’t require the remedial works, which the council claims.”