One of the seats was won by the Liberal Democrats in 1995 but lost to an Independent at a by-election following the death of the sitting member. The sitting Labour councillor, who had served on Carmarthen District Council since 1979, was de-selected by the party but was re-elected as an Independent Labour candidate.[2]
An unusual situation arose in this ward where the sitting Labour member (and previously a member of Dyfed County Council since 1981) announced shortly before the close of nominations that he would not stand and pledged his support to the Plaid Cymru candidate.
A by-election was held in the Llandybie ward following the death of Independent councillor Gerald Earl, who had represented the ward on the Dyfed and Carmarthenshire councils since 1973.