Opinion polls have given the centre-right, pro-business candidate, Donald Tusk, a slim lead over Warsaw's conservative mayor, Lech Kaczynski. Both have their roots in the Solidarity movement, which helped to bring down Communism in the 1980s.
Neither was expected to win outright and be able to avoid a second ballot in two weeks.
Yesterday's election follows parliamentary elections in which the two right-wing parties crushed the centre-left outgoing government, with Mr Kaczynski's party winning the most seats. The two parties are trying to form a coalition.
Mr Tusk's Civic Platform has campaigned for less red tape and taxes, while the more populist Mr Kaczynski and his Law and Justice party want greater state involvement in job creation.