Swansea council leader Lawrence Bailey has announced his resignation after Labour lost control of the authority following last week's elections.
Lawrence Bailey was 'bitterly disappointed' with the result
The party lost overall control of Swansea for the first time in 24 years with other parties refusing to work with them to form a coalition.
Mr Bailey said on Tuesday he would step down next week.
The Liberal Democrats are expected to take control along with an alliance of Conservatives and Independents.
Labour are still the biggest group, with 32 of the 75 councillors, but Lib Dems are second, with 19 members.
Lib Dems in neighbouring Bridgend have already formed a coalition with Conservatives and Independents.
Political horse-trading is continuing in councils across Wales after Labour lost control of several local authorities.
Labour had significant success in some areas, winning Rhondda Cynon Taf and Caerphilly back from Plaid Cymru, but it lost seats in a number of areas.
Nine of Wales' 22 county councils were left under no overall control.
Labour lost 13 councillors in Swansea, where the council had been criticised for closing the city's leisure centre.
The city's Lib Dems rejected a deal which would have kept Labour council leader Lawrence Bailey in power.
Lib Dem group leader Chris Holley said: "On 10 June the people of Swansea rejected years of Labour rule.
"It is now our duty to explore how to run the city and county in the best interests of the people of Swansea."
Who controls Welsh councils
Labour: 8 (Blaenau Gwent, Caerphilly, Flintshire, Merthyr, Neath-Port Talbot, Newport,
Independents: 3 (Anglesey,
Plaid Cymru: 1 (Gwynedd)
Conservatives: 1 (Monmouth)
No overall control: 9 (Bridgend, Cardiff, Carmarthenshire, Ceredigion, Conwy, Denbighshire, Swansea, Vale of Glamorgan, Wrexham)
Labour also lost seats in Wrexham, where it has 19 of the 52 seats, down from 23, while the Lib Dems have 10. Labour said it was still talking to the other parties.
In Cardiff - where high-profile Labour group leader Russell Goodway has resigned - the Lib Dems are the biggest group, with 33 of the 75 seats, to Labour's 27.
Cardiff Conservatives have ruled out coalition, and the Lib Dems may have to run the capital as a minority administration.
Anglesey is dominated by Independents, and they were meeting on Monday night in an attempt to decide who would lead a coalition.