It has unexpectedly been found that a low alcohol or alcohol-free beverage, with a flavor profile very close to a beer of at least 4% (vol/vol) alcohol, can be produced by using Pichia kluyveri yeast strains. In particular, Pichia kluyveri yeast strains only use the glucose in the wort, and have the ability of converting this substrate into a high concentration of specific flavor compounds, which are normally produced by Saccharomyces ssp. yeast strains used for the brewing of beer. In this way the Pichia kluyveri yeast strains can be used to produce either a low alcohol or alcohol-free beverage, depending on the glucose levels in the wort. The main flavor compounds produced by Pichia kluyveri in the fermentation of wort are isoamyl acetate, isoamyl alcohol, ethyl butyrate, ethyl hexanoate and ethyl octanoate.