When no party earns more than half of the vote in an election in South Africa, parties seek to get above that 50 percent threshold by forming coalitions, which allow them to control the council and choose a mayor. In Johannesburg over the past two years, parties in ruling coalitions have on multiple occasions fallen out with each other, leading to the creation of new alliances that install a new mayor.

“This is childish,” Junior Manyama, a disgruntled member of the city’s — and country’s — largest political party, the African National Congress, said as he smoked a cigarette in his car outside of City Hall earlier this month, waiting for council members to elect a new mayor.

Mr. Manyama, 31, was furious that his party, with 91 seats on the council, agreed to a power-sharing arrangement that allowed someone from a party that holds just three seats to lead South Africa’s largest city.

“We can’t trust these people anymore,” he said, referring to political leaders.

For about two decades after the first democratic elections in 1994, South Africans did not have to worry about these on-again, off-again political romances because the A.N.C. dominated at the ballot box, nationally and locally. But the party has recently lost hold of many major municipalities.