"It is my observation that all too many physicians -- mostly pediatricians -- are treating mild cases," he said. In addition, he said, they're using the drug as a preventive measure to fight the effects of household contacts with patients.
"It is not surprising that resistance is being seen," said he added, saying he'd be concerned "if there is a second wave of a more virulent mutated strain [this fall]."
Resistance to oseltamivir is more frequent in people treated with the drug, according to Dr. Daniel Hinthorn of the University of Kansas Hospital and Medical Center in Kansas City, Kansas.
If it shows up in a person who hasn't been exposed to the drug, it could be that it was transmitted from a person who had been given oseltamivir, he said.
The virus might also have undergone a genetic change to become resistant -- the "spontaneous mutation" Fukuda mentioned.
Or, the virus might have recombined with other strains -- something that influenza viruses do frequently –--and derived its resistance that way, Hinthorn said.
That's not very likely right now, he said, since the pandemic virus is just about the only strain in circulation.
"This is certainly potentially important," he said, but "only time will tell if this is a rare or a common event."
Oseltamivir is a member of a class of drugs known as neuraminidase inhibitors: neuraminidase in the "N" in H1N1. It's widely used because it is an oral drug. Its companion drug, zanamivir is inhaled, making it difficult to use for people with respiratory conditions. It is also not approved for children.
If oseltamivir resistance becomes widespread in the pandemic flu, it could create difficult treatment choices for physicians, according to Dr. Jeffrey Boscamp of Hackensack University Medical Center in Hackensack, N.J.
"We struggled during the seasonal flu outbreak this past winter with the emergence of Tamiflu-resistant influenza A and had to come up with some difficult antiviral combinations, particularly for children who couldn't take Relenza," he said.
"It is highly likely that we will see Tamiflu resistance here [in the pandemic strain] and it will limit our treatment options," he said. "It will be a very big problem if we see this novel virus becoming more virulent than it currently is."
All of this makes predicting what influenza will do a "dangerous game," according to Marc Lipsitch of the Harvard School of Public Health.
Even if it turns out that a resistant strain has been transmitted from one person to another, "it could be an unlucky, one-off event, and we need to watch and see how much more it spreads," he said.
And even if that's not so, it will take a while for resistance to become widespread, Lipsitch said.
"The use of oseltamivir will continue to have benefits for quite a while, because there are so many more drug-sensitive cases out there than drug-resistant ones," he said, "and we would expect it to be months at least -- maybe more -- before a resistant strain became a majority of cases."
"But predictions are hazardous and careful surveillance is critical," he added.
This article was developed in collaboration with ABC News.