The invention relates to a process for the preparation of a sugar product from ligno-cellulosic material, comprising the following steps: a) optionally pre-treatment of the ligno-cellulosic material; b) optionally washing of the optionally pre-treated ligno-cellulosic material; c) enzymatic hydrolysis of the optionally washed and/or optionally pre-treated ligno-cellulosic material using an enzyme composition comprising at least two cellulase and whereby the enzyme composition at least comprises GH61; and d) optionally recovery of a sugar product; wherein during part of the time of the enzymatic hydrolysis, oxygen is added to the ligno-cellulosic material and during part of the time of the enzymatic hydrolysis less oxygen is added to the ligno-cellulosic material compared to the other part of the time of the enzymatic hydrolysis, preferably no oxygen is added to the ligno-cellulosic material.