A process for the conversion of a solid material containing hemicellulose, cellulose and lignin, which process comprises the following steps: (i) hydrolyzing, at a temperature equal to or less than 40°C, preferably equal to or less than 30°C, at least part of the hemicellulose of the solid material by contacting the solid material with a first aqueous hydrochloric acid solution, which first aqueous hydrochloric acid solution has a hydrochloric acid concentration in the range from equal to or more than 15.0 wt. % to less than 40.0 wt. %, based on the weight amount of water and hydrochloric acid in such first aqueous hydrochloric acid solution, yielding a remaining solid material and an aqueous first hydrolysate product solution; (ii) displacing aqueous solution from the remaining solid material with a non-aqueous displacement fluid; (iii) hydrolyzing, at a temperature equal to or less than 40°C, preferably equal to or less than 30°C, at least part of the cellulose of the remaining solid material by replacing the non-aqueous displacement fluid with a second aqueous hydrochloric acid solution, which second aqueous hydrochloric acid solution has a hydrochloric acid concentration in the range from equal to or more than 40.0 wt. % to equal to or less than 51.0 wt. %, based on the weight amount of water and hydrochloric acid in such second aqueous hydrochloric acid solution, yielding a residue and an aqueous second hydrolysate product solution, wherein the process is carried out in one or more reactors and wherein the reactor comprises a cylindrical vessel with its axis arranged in an essentially vertical manner, and wherein said non-aqueous displacement fluid is a non-aqueous, preferably hydrophobic, liquid having a density equal to or less than 1000 kilograms per cubic meter (kg/m3), and wherein the non-aqueous displacement fluid is supplied to such reactor in a downward fashion. (i) hydrolyzing, at a temperature equal to or less than 40°C, preferably equal to or less than 30°C, at least part of the hemicellulose of the solid material by contacting the solid material with a first aqueous hydrochloric acid solution, which first aqueous hydrochloric acid solution has a hydrochloric acid concentration in the range from equal to or more than 15.0 wt. % to less than 40.0 wt. %, based on the weight amount of water and hydrochloric acid in such first aqueous hydrochloric acid solution, yielding a remaining solid material and an aqueous first hydrolysate product solution; (ii) displacing aqueous solution from the remaining solid material with a non-aqueous displacement fluid; (iii) hydrolyzing, at a temperature equal to or less than 40°C, preferably equal to or less than 30°C, at least part of the cellulose of the remaining solid material by replacing the non-aqueous displacement fluid with a second aqueous hydrochloric acid solution, which second aqueous hydrochloric acid solution has a hydrochloric acid concentration in the range from equal to or more than 40.0 wt. % to equal to or less than 51.0 wt. %, based on the weight amount of water and hydrochloric acid in such second aqueous hydrochloric acid solution, yielding a residue and an aqueous second hydrolysate product solution, wherein the process is carried out in one or more reactors and wherein the reactor comprises a cylindrical vessel with its axis arranged in an essentially vertical manner, and wherein said non-aqueous displacement fluid is a non-aqueous, preferably hydrophobic, liquid having a density equal to or less than 1000 kilograms per cubic meter (kg/m3), and wherein the non-aqueous displacement fluid is supplied to such reactor in a downward fashion.