Among those counting were the liberal Miami Herald, the liberal Los Angeles Times, the conservative Wall Street Journal and the conservative watchdog organization Judicial Watch.
Members of the organizations are not allowed to handle the ballots.
"Only our employees are allowed to touch the ballots. They hold them up and they look at them," said Mike Schotanus of the Broward County elections office.
Most of the organizations are recording in categories properly punched ballots, dimples and hanging chads and which is for which candidate.
Schotanus said the organizations were counting about 6,600 "undervotes" Monday. He said nobody knew whether they would finish by the end of the week.
"Undervote" is the term used for ballots with punch holes for other races but none for president. How these can then be "counted" is anyone's guess.
Broward, Miami-Dade and Palm Beach counties were the centers of the dispute over Florida's 25 electoral votes that eventually decided the election in favor of President-elect George W. Bush over Al Gore.
In Miami-Dade County, a recount of undervotes was also expected to begin Monday, but plans were incomplete. At a court hearing last week, the Miami Herald was told to come up with a plan, and another hearing was expected Thursday.
"There have been 22 requests for recounts," said Gisela Salas, of the Miami-Dade County elections office. "Nothing is firmed up yet, and it probably won't take place until next year."
In Palm Beach County, officials said the ballots had not yet been returned from the state capital of Tallahassee, and plans for a recount are incomplete.
Last month, Judicial Watch looked at 630 ballots in Palm Beach County.
Tom Fitton, president of Judicial Watch, said the organization had hired an accounting company to conduct the recount.
"We hope to get an independent set of numbers by an accounting firm we have a statistician here. We want to audit what went on beforehand so the people will know what went wrong in order to fix the system," Fitton said.
Several organizations, including Judicial Watch, plan to recount ballots in the entire state, but plans are still being made.
In Tampa, Fla., Hillsborough County Supervisor of Elections Pam Iorio said she doubted that a statewide review would be conclusive.
"There is the feeling that if only hand counts had been allowed to continue, we would know the truth," Iorio said. "But the truth is very elusive in this presidential race. And I think what we'll find is that the truth remains elusive."
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