Two Cardiff councillors have resigned from the authority's ruling Labour group in the space of two days.
Susan White has resigned from the council entirely, while Manzoor Ahmed has left the Labour group but will continue as an independent councillor.
Mr Ahmed alleged that the group was "rudderless" while Ms White has alleged "bullying" within the group.
Welsh Labour said its group had delivered new investment, and would investigate Ms White's claims.
Labour currently has a working majority of three - it had 17 more seats than the opposition after the last election.
The Liberal Democrats claimed the Labour group was in "crisis".
In a statement Mr Ahmed, who is a councillor for Adamsdown, said he was "extremely disappointed" not to be re-selected to stand in the 2017 council election, and described the selection process as a "disgrace".
The councillor said Labour council leader "Phil Bale has left Cardiff rudderless in stormy times", claiming he was "plainly incapable" and that the council would be better led by the Lib Dems.
"He has surrounded himself with a cabinet made up of the least able members of the Labour group and over half of them now openly agree that he is not a leader," he said.
Ms White, former councillor for Llandaff North, said she resigned from Cardiff council because of a "culture of bullying... which has been allowed to go unchecked for far too long".
She said she had experienced it "when I was the group secretary and, most recently, when I defended the Ahmadiyya Muslim Association (AMA)".
Her concerns grew, she said, when a colleague in the group "advised me not to accept an AMA invitation to an Eid dinner at Cardiff County Hall" because of a false allegation that the group were linked to the so-called Islamic State group.
She went on to attend the event.
Ms White said she had met "forceful opposition" when she had proposed a motion at a group meeting "merely stating that I had sought police advice and there was no valid reason for councillors not attending events such as the Eid dinner".
"I was sickened to the pit of my stomach that I encountered such heated resistance to my motion," she said, claiming not one member had supported her defence.
Ms White, who had planned to stand down at next May's local elections, resigned on Monday. There will be no by-election to replace her.
Rafiq Hayat of Ahmadiyya Muslim Community UK said the issues noted in the resignation statement by Ms White were "shocking", calling for Labour to investigate.
Cardiff Council deputy leader Sue Lent told BBC Wales Mr Bale has "no reason" to resign.
"Both resignations are nothing to do with his leadership," she said.
A Cardiff Labour group spokeswoman thanked Ms White for her commitment to her constituents.
"Cllr White's concerns were listened to and as a result the Council's approach to the AMA was amended," the spokeswoman said, adding others spoke in favour of AMA at the meeting Ms White discussed.
"We take all allegations of bullying seriously, and will work with Welsh Labour to look at the detail of Cllr White's statement," she said.
The group said it was regrettable Mr Ahmed had "jumped ship" after his de-selection by local Labour members in Adamsdown.
A spokesman for the Welsh Labour Party said: "Despite years of Tory imposed cuts, our councillors have delivered new investment in the city centre, helped schools to raise standards, and secured progress on a new bus terminal."
In response to Ms White's allegations, the spokesman said the party would work with the group to "fully investigate".
The Lib Dems said Labour had lost seven seats over the course of the term.
Cardiff council Lib Dem leader Judith Woodman said having lost councillors through resignations, defections and by-elections during this council term "it's clear Cardiff Labour are in crisis."