Construction workers in Western Australia are appealing to the Full Federal Court over a decision that could see dozens of workers fined more than $10,000 for attending a rally.

The Federal Court found last month that CFMEU members did not have permission from their employer to leave work on February 28, 2013.

The 76 workers walked off the job at the site of Perth's new Children's Hospital in Nedlands and attended a rally calling for more local jobs and apprenticeships, and greater Australian content in oil and gas projects.

An estimated 5,000 people from various unions attended the rally, which partially took place outside the Premier Colin Barnett's West Perth office building.

Fair Work Building and Construction (FWBC) initiated civil action last year, and last month the Federal Court ruled that 74 workers did contravene the Fair Work Act.

It is understood that the remaining two men did not respond to the court's initial summons and had no subsequent involvement in the case.

The maximum fine for an individual is $10,200, but the decision to appeal is expected to delay the imposition of any penalties.

The appeal is based on several grounds.

The CFMEU members say Justice Barker erred by suggesting an employee needed to prove they had authorisation to leave the site, and also failed to give consideration to the individual evidence of each of the men.

The members argue there was not enough evidence to prove each of them had breached the act.

In general terms, the workers allege FWBC did not prove their absence was not unauthorised.

A directions hearing is scheduled for October 19, with full hearings in the appeal expected next year.