nfectious-disease experts say problems could arise from the advice offered by Mayor Rudolph W. Giuliani and some doctors, who have suggested that people be vaccinated against influenza so they do not confuse early signs of inhalation anthrax with a case of the flu.

The main concern is that there is not enough vaccine for everyone, and if millions of healthy people get shots, they could keep the vaccine from those who need it most. That would be a much greater public health problem than inhalation anthrax, which has infected just 10 people.

The idea that flu vaccine might help prevent false alarms about anthrax came about because in its initial stages, inhalation anthrax seems much like the flu, causing fever, chills and muscle aches and pains.

So Mr. Giuliani and others suggested that if everyone got a flu shot, fewer people would get sick and clog doctors' offices and emergency rooms, worried that they had anthrax. Doctors would also run less risk of dismissing early signs of inhalation anthrax as the flu.

"All those people present the possibility of creating a lot of confusion in looking for an anthrax case," Mr. Giuliani said last week. "So it's good for you to get a flu shot, and it's really good for the city."

But, reasonable as that idea might sound, experts on infectious diseases say it may not be wise because there is not enough vaccine to go around. The top priorities for flu vaccine are the elderly; people with chronic diseases, especially heart or lung disease; people with weakened immune systems; pregnant women in their second or third trimesters; and health care workers.

"There's a real bottleneck right now because there isn't that much flu vaccine around," said Dr. Martin J. Blaser, an infectious-disease specialist at New York University School of Medicine. "If there were a run on vaccine so people at high risk couldn't get it, we're doing more harm than good."

The Centers for Disease Control and Prevention says that vaccine makers will produce more vaccine than ever this year — 85 million doses — but that production has been delayed and supplies are limited.

"I want to very clearly get across the message that the first group of people that we're most concerned about getting vaccine into are people who are at the highest risk for getting influenza," said Dr. Keiji Fukuda of the centers' influenza branch "We're not just telling people to just indiscriminately go out and get vaccinated."

Dr. Fukuda emphasized the vaccine's role: "We want people to get the flu vaccine to prevent influenza. We don't want to develop the implication that if you do develop a flulike illness that you ought to be more concerned about anthrax."

In fact, most people with flulike illnesses, tens of millions of cases each winter, have other viral infections, not the flu. And a flu shot will not prevent their sicknesses.

"If you look at everyone who comes into the office or emergency room with headache, cough and body aches, it would be just a small percent who have honest-to-God influenza," said Dr. Craig E. Smith, who is an infectious-disease specialist at Phoebe Putney Memorial Hospital in Albany, Ga. Dr. Smith, who is a member of the Infectious Disease Society of America's bioterrorism working group, said that what most of these ill people have instead is "other respiratory infections like parainfluenza virus, picorna viruses, adenoviruses."

And even if given a flu shot, a person could still get influenza, said Dr. Marguerite Neill, an infectious- disease specialist at Brown University. It takes a couple of weeks for immunity to kick in, so a vaccinated person can get the flu while the shot is taking effect. And the flu shots only protect against what are expected to be the dominant strains that year. The vaccines are 70 to 90 percent effective in preventing influenza.

Specialists in infectious diseases say they are worried about what they will do when the winter onslaught of patients with flulike illnesses hits. So far, Dr. Neill said, she and others have noticed symptoms that the inhalation anthrax patients did not have.

"They did not have stuffy or runny noses and they were not coughing up green or yellow mucus," she said. "Doctors can begin to take that kind of information as we all try to move forward. And we have to move forward. We have to figure out a way that we're going to get through this winter. And we all keep praying that there will be no new anthrax cases."