The invention is directed to a process for the conversion of cellulosic biomass, in particular lignocellulose-containing biomass into fermentable sugars. The invention is further directed to apparatus suitable for carrying out such processes. According to the invention biomass is converted into fermentable sugars by contacting in a reactor said biomass with an acid, while passing an inert gas stream capable of taking up water through said reactor, by which the pH in said reactor can be controlled.