In some Danish schools it is so widespread that the physical and mental welfare of 75 per cent of the pupils is said to be threatened.
The disparity has "shaken" Karen Jespersen, Denmark's minister of social affairs, who said "it is important that we make a great effort to combat bullying".
She will be discussing the effects on children at her next meeting with Ole Vig Jensen, minister of education, and Frank Jensen, minister of justice - the trio form the so-called secretariat against violence.
The Nordic survey revealed that 25 per cent of Danish pupils between the ages of 11 and 15 have been bullied (in Finland, it is 16 per cent; Norway: 15 per cent; Sweden: 6 per cent). A further 33 per cent of the same group admit they have bullied others (Finland: 11 per cent; Norway: 13 per cent; Sweden: 5 per cent).
The survey, which covered about 4,000 pupils in each country, also showed that children who were bullied were five times as likely to say that they were unhappy and 40 times as likely to say that they felt left out of things than pupils not bullied; they lacked self-confidence and found making friends very difficult.
"Bullying is a serious health problem," said Bjoern Holstein of the department of social medicine and psychosocial health at the University of Copenhagen, who conducted the survey at 45 Danish schools. "Bullying typically occurs at run-down schools where the teachers are so hard-pressed that they don't have the strength to stop it," he said. "Perhaps teaching posts haven't been filled, or there are too many pupils and too few teachers, or there is poor co-operation between teachers, principal and parents."
Bullying does occur in Sweden, but at a much lower and more evenly distributed level, said Mr Holstein, who is also professor of social medicine at the Nordic school of public health in Gothenburg.
"The difference arises because Sweden has a national policy of not accepting offensive behaviour towards children. Swedish schools are controlled centrally from Stockholm, and each school must prepare an action plan against bullying; in addition, preventing such behaviour forms part of Swedish school principals' work. In Denmark, it is up to the individual school to tackle the problem," said Mr Holstein.