The invention relates to a process for the production of crystalline xylose, from sugar cane bagasse, which xylose consists of microcrystals having a well-defined morphology and a narrow granulometric range, a further object of the invention being the protection of the product, crystalline xylose, manufactured according to the technological route which is detailed in the text of the patent. Additionally, the invention also relates to a process for obtaining crystalline xylitol with particularly adequate physical and functional characteristics, from the xylose produced according to the process idea conceived by the Applicant, as well as to the product proper, crystalline xylitol, generated in accordance with a particular sequence of unit operations. The process in question comprises an initial step for the formation of the xylose by means of an acid hydrolysis of the bagasse; a second step in which there is achieved the purification of the xylose solution thus formed; a third step in which there is accomplished the crystallization of the xylose by a controlled cooling of this said aqueous solution, thereby producing crystals with a xylose content higher than 99.0% by weight, on a dry solids basis; a fourth step which consists in the hydrogenation of the xylose and its consequent conversion to xylitol; a fifth step for the treatment and evaporation of the xylitol solution; and a last step for the crystallization of the xylitol, which is also carried out by a controlled cooling, thereby leading to the manufacture of crystals with a xylitol content which is never lower than 99.5% by weight, on a dry solids basis. The crystalline xylose and the crystalline xylitol produced according to the invention have remarkable degrees of purity, as pointed out, and exhibit, besides an excellent fluidity, a hygroscopicity and a dissolution time which confer on them an optimum performance when utilized in their industrial applications.