Dr John Hood, consultant bacteriologist at the infection control unit at Glasgow Royal Infirmary, said a man and woman in the hospital had been found to be carrying the bug.
He said that while the Staphylococcus aureus (MRSA) bug showed increased resistance to traditional antibiotics, it was not immune to them and said drugs were available to combat it.
He said: "This is not an outbreak. We have two separate organisms and they are not linked and the patients are not linked.
"It is colonising patients - it is not, as far as we know, infecting them - and it is not spreading. The existing guidelines in this hospital used for the prevention of the spread of MRSA have been shown to work."
Both patients were found to be carrying the germ during routine screening. One is in isolation and the other is at home. Both are described by the hospital as "not clinically infected" by the bug.
MRSA is carried by about 40 per cent of the population with the majority of carriers never developing symptoms or associated infections. It is usually treated by Vancomycin, but in recent years cases have been detected in Japan and the United States that have proved resistant to the drug.
The hospital placed one of the patients in isolation and took the precaution of banning all admissions to its intensive care unit between 3 and 8 June in an attempt to prevent the germ spreading. After it was confirmed no other patients were affected, the unit was reopened.
Dr Hood said: "We have isolated two distinct strains of methicillin-resistant MRSA from two patients. Further routine investigations, indicated they both showed increased resistance to Vancomycin."
He went on: "Such strains are extremely rare and have not been reported before in Scotland. The patients are presently not clinically infected and are on no antibiotics.
"If therapy is required other agents are available. A new drug is available to the hospital on a named patient basis.
"The difficulty with this particular strain of MRSA is that it may be more difficult to treat with Vancomycin and not that it is resistant to Vancomycin."Reuse content