The union says the complaints by Marjorie Marsh and Anne Russell will be the first in Scotland involving a white collar privatisation.
When law firm Harper Macleod took over from Stirling's in house solicitors on 1 July, three council lawyers were told to report for duty at the company's Glasgow offices. Only one turned up.
Unison District Chairman Gerry O'Reilly said last week that Mrs Marsh and Mrs Russell refused to accept the posting and reported for work at Stirling as usual.
Mr O' Reilly said if the women had agreed to become employees of Harper Macleod they would have lost conditions which they had enjoyed with the council, but which the private firm would not meet.
He said if the lawyers won their case councils would have to 'think very carefully' before privatising more services.
The decision of Tory controlled Stirling to employ Harper Macleod made it the first council in Scotland to privatise its legal department.
A council spokesman confirmed the two women had withdrawn complaints under the council's internal grievance procedure in favour of an industrial tribunal.