SIPTU members placed pickets on a Co Cork biopharmaceutical plant in a dispute over union recognition.
Several hundred people are understood to be employed there.
SIPTU says the Labour Court has ruled in favour of its members in relation to the dispute, but that the company, which is listed on the New York Stock Exchange, is refusing to engage, or to implement the Labour Court recommendation.
The union says the dispute has been ongoing for more than a decade.
Three 36-hour work stoppages are due to take place at the plant this month, with the first one today.
They will be followed by a 33-hour work stoppage by SIPTU members beginning at 7am on 7 December and a 48-hour stoppage on 11 December.
It is understood that operations at AbbVie's two other manufacturing plants in Co Sligo and its offices in Dublin are not affected by the dispute.
A spokesman for AbbVie said the company is disappointed with what it considers an unnecessary course of action.