NOVELTY - Producing furfural, 5-hydroxymethylfurfural, and/or levulinic acid from cellulosic biomass, involves: (a) providing a feedstock comprising lignocellulosic biomass; (b) in a digestor, fractionating the feedstock under effective fractionation conditions in the presence of a solvent for lignin, sulfur dioxide, and water; (c) hydrolyzing the hemicellulose contained in the liquor; (d) dehydrating the hemicellulose and/or the hemicellulosic monomers; and (e) converting at least some of the 5-hydroxymethylfurfural to levulinic acid and formic acid.    USE - The process is useful for producing furfural, 5-hydroxymethylfurfural, and/or levulinic acid from cellulosic biomass (claimed). It can also be used for producing other sugar-derived products.    ADVANTAGE - An advantage of the process is that it produces cellulose-rich solids while concurrently producing a liquid phase containing a high yield of both hemicellulose sugars and lignin, and low quantities of lignin and hemicellulose degradation products. The flexible fractionation technique enables multiple uses for the products. The cellulose is highly reactive to cellulase enzymes for the manufacture of glucose. Other uses for celluloses can be adjusted based on market conditions.    DETAILED DESCRIPTION - Producing furfural, 5-hydroxymethylfurfural, and/or levulinic acid from cellulosic biomass, involves: (a) providing a feedstock comprising lignocellulosic biomass; (b) in a digestor, fractionating the feedstock under effective fractionation conditions in the presence of a solvent for lignin, sulfur dioxide, and water, to produce a liquor containing hemicellulose, cellulose-rich solids, and lignin; (c) hydrolyzing the hemicellulose contained in the liquor, under effective hydrolysis conditions, to produce hemicellulosic monomers; (d) dehydrating the hemicellulose and/or the hemicellulosic monomers under effective dehydration conditions to convert at least a portion of C5 hemicelluloses to furfural and to convert at least a portion of C6 hemicelluloses to 5-hydroxymethylfurfural; (e) converting at least some of the 5-hydroxymethylfurfural to levulinic acid and formic acid; and (f) recovering at least one of the furfural, the 5-hydroxymethylfurfural, or the levulinic acid; or producing furfural, 5-hydroxymethylfurfural, and/or levulinic acid from cellulosic biomass, involves: (a) providing a feedstock comprising lignocellulosic biomass; (b) in a digestor, fractionating the feedstock under effective fractionation conditions in the presence of a solvent for lignin, sulfur dioxide, and water, to produce a liquor containing hemicellulose, cellulose-rich solids, and lignin; (c) dehydrating the hemicellulose under effective dehydration conditions to convert at least a portion of oligomeric C5 hemicelluloses to furfural and to convert at least a portion of oligomeric C6 hemicelluloses to 5-hydroxymethylfurfural; and (d) recovering at least one of the furfural or the 5-hydroxymethylfurfural.