A method for producing a strain of Saccharomyces cerevisiae with introduced genes coding for xylose reductase, xylitol dehydrogenase and xylulokinase and with improved ethanol production, improved xylose conversion and reduced xylitol production is described. The method comprises culturing the cells in a repetitive batch series in a medium at a xylose concentration of about 15-25 g / l and at a temperature of about 28-32° C., and thereafter lowering the xylose concentration in at least one step at a temperature of about 28-32° C. to obtain an increased selection pressure for improved xylose fermentation,improved ethanol production and reduced xylitol production, and continuing the culturing of the cells in said repetitive batch series. Further, strains of Saccharomyces cerevisiae obtained by the method according to the invention are described.