The present invention concerns an acohol free or low alcohol beer having an alcohol content of not more than 0.7 vol.%, characterized by a relationship y ‰¥ A x b wherein A = 0.25 and b = 1.5, and wherein €¢ x is the ratio between unfermentable over real extracts, wherein the unfermentable extract is the value of the real extract less the total content of real sugars, which consist of fructose, maltose, glucose, maltotriose, and saccharose, and €¢ y is the ratio between the combined content of maltopentaose, maltohexaose, and maltoheptaose over the total amount of main sugars, wherein the main sugars consist of fructose, maltose, glucose, saccharose, maltotriose, maltotetraose, maltopentaose, maltohexaose, and maltoheptaose. It also concerns a method for producing an acohol free or low alcohol beer comprising €¢ Preparing a wort (23) of fermentability not higher than 29%, preferably, not higher than 25%, more preferably at most 20%; and €¢ Fermenting the thus prepared wort in a fermentation tank (4) by a cold contact process.