Many, including Russia, are among the 44 countries taking part in the council's educational programmes. The region faces the danger of new forms of intolerance, racism and political extremism after the collapse of communism, the council believes.
But schools can help to avert such threats, and the teaching of history plays a central role, says the council, which last year ran a European Youth Campaign Against Intolerance .
Failing to adopt a balanced approach to history teaching could result in the emergence of a cynical and vulnerable generation prey to extreme ideas, says the council in a new publication.
Carmel Gallagher, principal officer for history at the Northern Ireland Council for the Curriculum, Examinations and Assessment, and author of the new booklet, History Teaching and the Promotion of Democratic Values and Tolerance, seems well-qualified to comment having spent 10 years as head of history at a school in the Falls Road, Belfast.
"In Northern Ireland history teachers have to be very careful to put a range of points of view across so that pupils at least have the opportunity to consider perspectives they would not normally come into contact with," she says.
"It's important in the emerging democracies where there is a desire to create a sense of pride in the past. That's legitimate as long as they are not shoring up prejudices and hatred against others."
The booklet challenges the view of school history as "a body of knowledge to be learned and regurgitated" and recommends instead a "process" approach, based on inquiry and problem-solving, which encourages "critical thinking based on a study of evidence and varying perspectives".
Practical advice includes an outline of the kinds of historical evidence young people might be presented with and the skills they need to interpret it - who made or wrote it, what position did heshe hold, when was it written and in what political context, and so on.
Some may argue that there is little sense in replacing a view of history based on an absolute set of values with one that attempts to be value-free. The spectre of relativism is hovering over Europe, they may well warn.
However, Ms Gallagher says: "History teachers have a responsibility to encourage children to think for themselves instead of believing everything they are told."
History Teaching and the Promotion of Democratic Values and Tolerance, by Carmel Gallagher, available free from the education department, Council of Europe, F-67075, Strasbourg, CEDEX, France.