The Liberal Democrats and Labour are set to open talks about forming an alliance to run Oxfordshire County Council after the Conservatives suffered big local election losses.
The Tory group remains the largest on the authority, with 22 seats after losing nine but is short of the 32 needed for a majority.
The Lib Dems won 21 and Labour 15, giving the parties enough to make an administration if they work together.
Talks will be held over the next week.
Lib Dem leader Richard Webber told the BBC his party's "first exercise" was to "cement" its alliances with the three Green councillors before entering coalition talks with Labour.
He said his team was sifting through each party's manifesto to identify "potential clashes" on policies and areas where agreements could be made.
The Lib Dem leader said any alliance depended on "what each person desires" but added he believed it was "high unlikely" any deal would be made with the Conservative group.
"We are hoping that we can find enough common ground with Labour in particular," he said.
However, Mr Webber said regardless of the outcome of the talks, he would step down as leader of the Lib Dems and would not try to become leader of the council.
The councillor, who has led the Oxfordshire group for seven years, said a Lib Dem leadership election would be held on Saturday.
Mr Webber said he would be "devoting" himself to his ward of Sutton Courtenay and Marcham but would be open to a role in a new administration.
Liz Brighouse, leader of the Labour group, said she would "have to see what was on the table" from all parties.
She said: "The main thing is delivering on what we promised (in our campaign)."
However, the Labour leader admitted her party and the Conservatives had been "poles apart" in recent years.
Analysis: BBC Oxford political reporter Bethan Nimmo
The Conservatives and Liberal Democrats ended up with almost a dead heat once votes were counted this weekend - with 22 seats and 21 seats respectively.
So whoever wants to take power will first have to make some friends.
The most likely scenario at the moment seems to be a pact between the Lib Dems, Greens and Labour.
That would be pretty historic - at no point have the Conservatives on Oxfordshire County Council ever been in opposition.
Among the Tory councillors who lost their seats was Ian Hudspeth, the county council's leader since 2012. He was also chair of the Community and Wellbeing Board at the Local Government Association.
Mr Hudspeth, a councillor since 2005, lost his Woodstock seat to Lib Dem Andy Graham in a shock result by 168 votes.
"I'm really disappointed because I've loved representing the residents of Woodstock for the past 16 years, I felt I've done a good job for them," he said.
"Obviously they've decided they want a change and I accept it because I'm a democrat and I believe in the democratic process."