They resulted in a coalition between Independent councillors and Plaid Cymru for the next five years.
The Liberal Democrats won both seats in 1995 but Labour captured one of these in a by-election following the death of a sitting member.
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.
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.
No boundary changes but an additional seat created 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.