Employees' e-mail and Internet activities are being tracked by an increasing number of employers, according to the Manufacturing, Science, Finance Union (MSF).
The union membership is mainly in the financial services sector.
Its Irish secretary, Mr Jerry Shanahan, has called for legislation at national and EU level to limit the increasing use of electronic surveillance by employers in the workplace.
MSF accepts that employers have a right to monitor e-mail or visits to Internet sites if there is reasonable suspicion that an employee "has committed a criminal or disciplinary offence, or is in breach of an agreement".
Mr Shanahan says some employers "routinely" monitor electronically-based activities in the workplace, including trade union activities.