The invention relates to a process for the preparation of a fermentation product from lignocellulosic material, comprising the following steps: a)optionally,pre-treatment of the lignocellulosic material, b)optionally, washing of the optionally pretreated lignocellulosic material, c)enzymatic hydrolysis of the optionally washed and/or optionally pretreated lignocellulosic material using an enzyme composition comprising at least two cellulases and whereby the enzyme composition at least comprises LPMO, and optionally purifying the hydrolysed lignocellulosic material, d)fermentation of the hydrolysed lignocellulosic material to produce a fermentation product,and e)optionally,recovery of a fermentation product, wherein oxygen is consumed in amounts corresponding to between 20 and 5000 mmol molecular oxygen per kg glucan present in the lignocellulosic material, the oxygen is added after the pretreatment and before and/or during the enzymatic hydrolysis of the lignocellulosic material, preferably in an amount corresponding to at least 30 mmol molecular oxygen per kg glucan present in the lignocellulosic material, more preferably in an amount corresponding to at least 40 mmol molecular oxygen per kg glucan present in the lignocellulosic material, and most preferably in an amount corresponding to at least 50 mmol molecular oxygen per kg glucan present in the lignocellulosic material is consumed.