Independent councillor George Black criticised West Dunbartonshire officers' impartiality on the council's Facebook site while Socialist Jim Bollan also did so on a publicly accessible website, an investigation has concluded.
Bill Thomson, Commissioner for Ethical Standards in Public Life in Scotland, found both had breached the councillors' code of conduct.
Mr Thomson said Mr Black's contravention was in connection with postings made on the council's Facebook site, "questioning the impartiality and capability of officers".
Mr Bollan's contravention related to his conduct on the web.
Their cases have been referred to the Standards Commission for Scotland.