In Arklow, TK Maxx workers represented by the Mandate trade union are on strike today.
The row centres on what the union describes as the company's refusal to agree to a Labour Court recommendation to hold talks.
The union concedes that the company has made some improvements to pay, hours and rostering, but says talks are needed to resolve outstanding issues.
Mandate's Michael Meegan says today's strike action could escalate: "The pickets are going on from 9 o'clock until 7 o'clock at the Arklow store.
"We will be reviewing that with a view of putting more pickets on at a time that suits the members and a view to maybe looking at other stores and seeing if they would be willing to come out in support of these other members as well."