Two Madonna fans are suing the megastar for damages over concerts in New York that started two hours late, accusing her of "flippant difficulty", court documents show.

Michael Fellows and Jonathan Hadden are suing Madonna as well as touring giant Live Nation and New York City venue the Barclays Center for an unspecified amount over late starts of her Celebration Tour gigs in December 2023.

"The concerts at the Barclays Center were advertised to start at 8:30pm, but Madonna did not take the stage until after 10:30pm on all three nights, with most concert attendees leaving the Barclays Center after 1am," read the court documents obtained on Friday.

"Madonna had demonstrated flippant difficulty in ensuring a timely or complete performance … (that) resulted in the ticketholders waiting for hours for the concerts to begin.

"Others were left stranded in the middle of the night because they missed their arranged ride home or public transportation."

The complaint, filed in a Brooklyn federal court on Wednesday, alleges that "Madonna has a long history of arriving and starting her concerts late, sometimes several hours late".

The Barclays Center, Live Nation and a representative for Madonna did not respond to requests for comment.

A bacterial infection that left Madonna in intensive care in 2023 meant her 84-date Celebration tour was postponed, forcing the delay of the New York dates at the centre of the litigation to December 2023.

The Grammy-winning icon behind classics including Like A Virgin and Material Girl has asserted incalculable influence as one of music's top stars.

In 2020, she underwent hip replacement surgery following an injury sustained on her Madame X tour.