Tires for vehicle wheels having reduced environmental impact and the components thereof, in particular reinforcing structural elements such as carcass structures, belt structures, flippers and chafers, include elongated reinforcing elements treated with resorcinol and formaldehyde-free cross-linkable adhesive compositions. The adhesive compositions include at least a) a rubber latex, at least b) an epoxide and at least c) a polyamine with molecular weight higher than 190 Daltons, including at least two amino groups selected from primary —NH2 and secondary —NH— amino groups. In the structural element, these compositions confer an adhesion between cords and compounds that is comparable to, if not better than, the traditional RFL system in use in this sector. Furthermore, by suitably modifying the compound compositions in the reinforced structural elements and, possibly, also in the other elastomeric components of the tire, it is possible to manufacture tires while avoiding the use of toxic chemicals, such, as resorcinol and formaldehyde.