Abstract: An alkali aluminosilicate geopolymeric matrix for the production of composite materials with a fiber reinforcement has a composition, after dehydration, expressed as oxides, as follows:yM.sub.2 O:Al.sub.2 O.sub.3 :xSiO.sub.2where "x" is 6.5-70, "y" is 0.95-9.50 and M is Na, K or Na+K. The geopolymeric matrix comprises a nanocomposite material with at least two phases, with (a) a first nodular silicious phase composed of nanospheres with diameters of less than 1 micron, preferably less than 500 nm, and (b) a second polymeric phase essentially composed of alkali poly(aluminosilicate) having one or more sialate bridge (--Si--O--Al--O) cross-linking sites of total formula M.sub.4 Si.sub.2 AlO.sub.10 to M.sub.2 Si.sub.4 AlO.sub.16, such that, in the alkali poly(aluminosilicate), the ratio of Si(O.sub.4) to Al(O.sub.4) is >3.5, preferably >5. The geopolymeric matrix has a spectrum of .sup.29 Si MASNMR with three resonance regions: -87.+-.5 ppm, -98 .+-.5 ppm, -107 .+-.