The virus currently causing bird flu in humans appears to be developing resistance to the drug selected to combat the infection.
Tamiflu is the only drug known to be effective against bird flu
Oxford University researchers report two cases of patients in Vietnam who died after failing to respond to treatment with the drug Tamiflu.
Details are published in the New England Journal of Medicine.
The H5N1 variant of the bird flu virus has so far killed over 70 people in south east Asia.
Most of the victims were in close contact with infected birds, and at present the virus is not believed to pose a significant threat to the wider population.
The latest deaths have been seen in Indonesia, where two more people have died from the virus, bringing the total there to 11.
Experts fear the virus will mutate and gain the ability to pass easily from human to human.
If this happens, they fear a global flu pandemic, which could kill millions world-wide.
A previous paper in the journal Nature described a single case of drug resistance in a patient being treated for avian flu.
However, in this case the patient had been given low doses of Tamiflu before becoming infected, as a family member had been stricken.
Lead researcher Dr Jeremy Farrar described the latest findings as "very worrying" - but said they were not surprising.
He said all microbes, whether parasites, bacteria or viruses, eventually started to develop drug resistance.
He said: "If this virus was to develop drug resistance and the ability to go from one person to another, that would clearly be a major problem."
However, Dr Farrar said there was some evidence to suggest viruses that developed drug resistance were also less likely to gain the ability to jump from person to person.
But he said the Vietnam findings stressed the importance of making sure the drug was only used in appropriate cases.
"We don't have a back-up at the moment, so we can't combine it with another drug, as we would with HIV, to prevent drug resistance developing."
Professor John Oxford, an expert in virology at Barts and The London Medical School, Queen Mary's School of Medicine, said: "This study shows again what a threatening virus it is.
"Vietnam is on the front line and anything we can learn from what is going on there will benefit us when the virus arrives on our shores."
Professor Oxford called for more investment in developing new drugs to combat the virus.
However, he said the Vietnam study did show that Tamiflu could be an effective treatment if given at any time up to five days after infection becomes apparent.
Previously, it had been thought that the drug had to be administered with 48 hours to have a profound effect.
He also said the study confirmed that the higher the level of infection with the H5N1 virus, the more severe a patient's symptoms were likely to be.
A Department of Health spokesperson said the paper would be considered carefully.
"The drug needs to be used carefully and appropriately to minimise the risk of resistance.
"The government is taking steps to build up a stockpile of antiviral drugs to treat those who are ill in a pandemic, and we would agree with the authors that people should not privately stockpile the drug as this risks increasing resistance.
"Tamiflu was chosen on the basis of independent expert advice that reflected its efficacy and ease of administration.
"Our antiviral strategy is kept under constant review and we are looking carefully at Relenza as a possible back-up to Tamiflu."