Vulcanisable elastomeric composition for components of tyres comprising at least: a) 100 phr of at least one diene elastomeric polymer, b) from 1 to 80 phr of modified silicate fibres with needle-shaped morphology of nanometric size, wherein said fibres have an aspect ratio of at least 2:1 and a diameter or maximum cross-sectional dimension of less than 500 nm, said modified fibres being at least partially coated with amorphous silica deposited on the surface, (c) from 0 to 120 phr of a standard reinforcement filler, (d) from 0.1 to 15 phr of a vulcanising agent, and (e) from 0.1 to 20 phr of a coupling agent, wherein said modified fibres are obtainable according to a process that comprises: - providing silicate fibres with needle-shaped morphology of nanometric size having an aspect ratio of at least 2:1 and a diameter or maximum cross-sectional dimension of less than 500 nm, - suspending said fibres in a first liquid medium, - placing the suspension of the fibres in contact with a compound precursor of amorphous silica, possibly dissolved or suspended in a second liquid medium, wherein said compound precursor of amorphous silica is selected from: I. the alkaline salts of silicic acid, of formula M 2 O. n SiO 2 where M = Na, K, Li and where n is comprised between 0.5 and 4, preferably n =0.5 or 1 or 3 and M=Na or K; II. the tetra-alkyl derivatives of silicic acid (or tetra-alkoxy-silanes) of formula 4 Si wherein the R groups, equal to or different from each other, represent C1-C6 alkyls, III. the halosilanes of formula SiX 4 or 3 SiX or 2 SiX 2 or SiX 3 wherein the R groups, equal to or different from each other, represent C1-C6 alkyls, and X, equal to or different from each other, are selected from among chlorine, bromine and iodine, preferably chlorine; - possibly providing water, - possibly providing an acid or a base, - hydrolyzing the compound precursor of amorphous silica and allowing the modification of the fibres, and - separating the fibres thus modified from the final liquid medium. a) 100 phr of at least one diene elastomeric polymer, b) from 1 to 80 phr of modified silicate fibres with needle-shaped morphology of nanometric size, wherein said fibres have an aspect ratio of at least 2:1 and a diameter or maximum cross-sectional dimension of less than 500 nm, said modified fibres being at least partially coated with amorphous silica deposited on the surface, (c) from 0 to 120 phr of a standard reinforcement filler, (d) from 0.1 to 15 phr of a vulcanising agent, and (e) from 0.1 to 20 phr of a coupling agent, - providing silicate fibres with needle-shaped morphology of nanometric size having an aspect ratio of at least 2:1 and a diameter or maximum cross-sectional dimension of less than 500 nm, - suspending said fibres in a first liquid medium, - placing the suspension of the fibres in contact with a compound precursor of amorphous silica, possibly dissolved or suspended in a second liquid medium, wherein said compound precursor of amorphous silica is selected from: I. the alkaline salts of silicic acid, of formula M 2 O. n SiO 2 where M = Na, K, Li and where n is comprised between 0.5 and 4, preferably n =0.5 or 1 or 3 and M=Na or K; II. the tetra-alkyl derivatives of silicic acid (or tetra-alkoxy-silanes) of formula 4 Si wherein the R groups, equal to or different from each other, represent C1-C6 alkyls, III. the halosilanes of formula SiX 4 or 3 SiX or 2 SiX 2 or SiX 3 wherein the R groups, equal to or different from each other, represent C1-C6 alkyls, and X, equal to or different from each other, are selected from among chlorine, bromine and iodine, preferably chlorine; I. the alkaline salts of silicic acid, of formula M 2 O. n SiO 2 where M = Na, K, Li and where n is comprised between 0.5 and 4, preferably n =0.5 or 1 or 3 and M=Na or K; II. the tetra-alkyl derivatives of silicic acid (or tetra-alkoxy-silanes) of formula 4 Si wherein the R groups, equal to or different from each other, represent C1-C6 alkyls, III. the halosilanes of formula SiX 4 or 3 SiX or 2 SiX 2 or SiX 3 wherein the R groups, equal to or different from each other, represent C1-C6 alkyls, and X, equal to or different from each other, are selected from among chlorine, bromine and iodine, preferably chlorine; - possibly providing water, - possibly providing an acid or a base, - hydrolyzing the compound precursor of amorphous silica and allowing the modification of the fibres, and - separating the fibres thus modified from the final liquid medium.