The present invention relates to a process for producing an oxidized cellulose pulp fibrillar network and a composite with lignocellulosic fibers comprising the following steps: (a) oxidizing a cellulose pulp to obtain about 0.3 to 2.5 mmol carboxylic groups per gram cellulose pulp; and about 0.1 to 5.0 mmol aldehyde groups per gram cellulose pulp; (b) homogenization of the cellulose pulp of step (a) wherein the cellulose fibers are refined to provide a cellulose pulp comprising 0-50% of fibers having an average length 0.7 mm-2.1 mm; and 50-100% of fibers having a particle size of 0.05-500 micrometer (μm); and optionally (c) combining with lignocellulosic fiber. Also step (d) drying of the cellulose pulp obtained by step (b) or step (c) may be included in the process.