The next round in the ongoing dispute between British Airways and the Unite union is set to go ahead on Thursday.
The union will learn if its appeal against an injunction stopping planned strikes has been successful.
If the judges accept Unite's appeal, then the strikes are free to go ahead, possibly from as early as next week.
But if the judgement goes against Unite, it has indicated it will hold another ballot of cabin crew in the row over pay, jobs and working conditions.
It would be the third such ballot since November last year, with the first two ballots declared invalid by the High Court.
On Monday a High Court judge ruled that Unite had failed to properly inform its members about the 11 spoilt ballot papers in the last strike vote.
Three senior judges, including the Lord Chief Justice, heard the union's arguments on Tuesday seeking to overturn the injunction and the reserved judgement will be handed out at 0930 BST.
Despite the ruling in favour of BA on Monday, flights have been disrupted with the airline unable to reinstate all flights.
The first Unite strike had been scheduled to begin on Tuesday, ending on 22 May, with the three further strikes planned to begin on 24 May, 30 May and 5 June.