The present invention relates to processes for producing fermentation products from starch-containing material, wherein an alpha-amylase and optionally a thermostable protease, pullulanase and/or glucoamylase are present and/or added during liquefaction, wherein a cellulolytic composition is present and/or added during fermentation or simultaneous saccharification and fermentation. The invention also relates to a composition suitable for use in a process of the invention.