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Staff are entering the fourth week of indefinite strike action over the threat of their jobs being outsourced as part of the council's £100m Service@Swansea IT project.
The council and representatives of the IT workers' union Unison held informal talks last week and more talks have been scheduled for this week.
Unison claimed that Swansea's council tax system had been affected by the dispute, but the council denied this. A council spokesman said, "The industrial dispute is continuing but IT services are continuing normally."