The invention concerns a cellulose fiber of the genus Lyocell which is treated with a cross-linking agent, with the cross-linking agent inducing a protection from fibrillation on the fiber and exhibiting the following properties: the protection from fibrillation induced by the cross-linking agent changes if the fiber is stored within a pH range from 4.0 to 10.0, in particular under the influence of moisture and/or heat, within the pH range from 4.0 to 10.0, an optimum value exists at which the stability of the protection from fibrillation induced by the cross-linking agent during storage is highest a suitable range exists around the optimum value in which the stability is reduced by 20% at the most, compared to the stability at the optimum value, within the pH range from 4.0 to 10.0, the suitable range is limited by at least one limiting value at which the stability is reduced by 20% compared to the long-term stability at the optimum value and with a further decrease in stability occurring below and above said value, respectively, and the cross-linking agent has the capability to change the pH value. The fiber according to the invention is characterized in that the fiber comprises a buffering substance in the suitable range and exhibits a buffer capacity of at least about 12 mmol/kg fiber, preferably from about 15 to about 70 mmol/kg fiber, in the suitable range.