The 65-year-old megastar played concerts at the Barclays Centre in Brooklyn for the North American leg of her Celebration tour in December which fans Michael Fellows and Jonathan Hadden attended.
Documents to the United States District Court for the Eastern District of New York say that Madonna "demonstrated flippant difficulty in ensuring a timely or complete performance" and the start time of 8.30pm was "optimistic speculation".
They say the concert began on December 13 2023, between 10.45pm and 11pm, and finished after 1am New York time.
Mr Fellows and Mr Hadden, who are represented by lawyers Richard Klass and Marcus Corwin, said that due to the event taking place on a Wednesday, there were issues getting home for concertgoers.
The documents say "many ticketholders who attended concerts on a weeknight had to get up early to go to work and/or take care of their family responsibilities the next day" and there was limited access to public transportation or ride-sharing apps.
The Barclays Centre and Live Nation were also named in the court filing.
"Defendants failed to provide any notice to the ticketholders that the concerts would start much later than the start time printed on the ticket and as advertised, which resulted in the ticketholders waiting for hours," the documents state.
The filing also claims "Madonna has a long history of arriving and starting her concerts late, sometimes several hours later" while citing her 2015 to 2016 Rebel Heart tour and her 2019 to 2020 Madame X tour.
They also say other timings were delayed at the Barclays Centre and other stops as part of the Celebration tour.
Mr Fellows, who paid $US155.90 ($A236.53) for his ticket, and Mr Hadden, who bought two tickets for $US292.50 ($A443.77), have asked for a jury trial in the case.
Madonna told a Las Vegas audience in 2019 that "a queen is never late" in a video she shared following a lawsuit claiming lateness.
The previous case was dismissed.
Her Celebration tour, featuring her greatest hits, was rescheduled last year due to her stay in intensive care over a "serious bacterial infection".
The singer subsequently announced that the dates for North American shows had been changed and kicked off her tour in London in October at The O2.
Her next tour date is at the Bell Centre in Montreal, in Canada, on Saturday and Madison Square Garden in New York on Monday.
The Barclays Centre, Madonna and Live Nation have all been asked for comment.
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