Opposition leader Bassirou Diomaye Faye is leading the race in Senegal's presidential election, according to local media.
Several of the 17 candidates have conceded to him, however official results have not yet been announced.
Millions took part in a peaceful vote on Sunday, following three years of turbulence and opposition protests against the incumbent, Macky Sall.
The ruling coalition's choice, Amadou Ba, has denied that he has lost.
He said he expected to contest a run-off vote to decide a winner. This would be required if no candidate gets more than 50% of the vote.
Mr Faye, 44, a senior official in the Pastef party led by Ousmane Sonko, had been in jail until 10 days before the vote. Mr Sonko was disqualified from the race because of a defamation conviction, which he said was politically motivated.
The first set of tallies announced on television showed Mr Faye had won the majority of votes, triggering widespread street celebrations in the capital, Dakar.
Supporters set off fireworks, waved Senegalese flags and blew vuvuzelas.
The results led to five opposition candidates declaring Mr Faye the winner. Anta Babacar Ngom, the only female candidate, wished Mr Faye success in a statement.
Mr Faye has not yet commented.
The results being announced are from local media tallying the results posted outside individual polling stations.
It is not clear how many of the 15,633 polling stations have been counted so far. Official results are expected by Tuesday.
Mr Sonko backed Mr Faye, the co-creator of his now dissolved Pastef party, who was also detained almost a year ago on charges including defamation and contempt of court.
An amnesty law passed this month allowed their release days before the vote.
They have campaigned together under the banner "Diomaye is Sonko". Some high-profile politicians and opposition candidates have backed Mr Faye's candidacy.
"The population is choosing between continuation and rupture," Mr Faye said after casting his vote, urging contenders to accept the winner.
Prepare for run-off
Mr Sall, the incumbent, was not on the ballot for the first time in Senegal's history. His ruling coalition picked Mr Ba, 62, a former prime minister.
Mr Ba's campaign said that "considering the feedback of the results from our team of experts, we are certain that, in the worst-case scenario, we will go to a run-off".
About 7.3 million people were registered to vote in the country of around 18 million.
The election had been due to take place last month but Mr Sall postponed it, triggering deadly opposition protests.