Heads claim they are unfairly paid around pound;7,000 less for doing similar work and allege the difference is due to sex discrimination. Most primary heads are women and most secondary heads men.
Around 580 primary heads have submitted claims under the Equal Pay Act 1970, backed by the Association of Head Teachers in Scotland, which could cost councils about pound;70 million if they win.
All councils are fighting the test case of three South Ayrshire heads by contributing to the legal costs of the local authority.
Anne Nutt, Kingcase primary, Prestwick; Stella Morton (now retired), Forehill primary, Ayr and Paige Paterson, Girvan primary, are claiming pay parity with heads of Carrick Academy, Maybole; Mainholm Academy, Ayr and Mallaig High in Highland. The primaries and secondaries have similar roll numbers of 500-600.
The tribunal this week heard a number of legal submissions from the local authority.