Tyre for vehicle wheels, comprising: a carcass structure comprising at least one carcass ply formed by a plurality of strip-like elements in circumferential side by side relationship, wherein axially opposite end flaps of said at least one carcass ply are engaged to respective annular anchoring structures , wherein a lateral longitudinal portion of each strip-like element is superimposed on a lateral longitudinal portion of an adjacent strip-like element such as to form a joint, wherein at least at the sidewalls of the tyre , said at least one carcass ply forms two superimposed layers; a belt structure located in a radially external position with respect to the carcass structure ; a tread band located in a radially external position with respect to the belt structure ; wherein each strip-like element comprises a plurality of first cords in a side by side relationship, located in a central part of the strip-like element and each exhibiting a first average diameter (d1); wherein each of the lateral longitudinal portions of each strip-like element exhibits a reduced thickness (S2) with respect to a thickness (S1) of the central part of the strip-like element ; wherein each of the lateral longitudinal portions of each strip-like element comprises at least one second end cord with a second average diameter (d2) that is smaller than said first average diameter (d1), the respective joint exhibiting a thickness that is substantially equal to the thickness (S1) of the central part of the strip-like element ; wherein each of the lateral longitudinal portions exhibits, in a transversal section to the longitudinal development of the strip-like element , at least a connecting step between the respective lateral longitudinal portion and the central part of said strip-like element ; wherein the step is one on each longitudinal portion , the two longitudinal portions of a single strip-like element being asymmetric. a carcass structure comprising at least one carcass ply formed by a plurality of strip-like elements in circumferential side by side relationship, wherein axially opposite end flaps of said at least one carcass ply are engaged to respective annular anchoring structures , wherein a lateral longitudinal portion of each strip-like element is superimposed on a lateral longitudinal portion of an adjacent strip-like element such as to form a joint, wherein at least at the sidewalls of the tyre , said at least one carcass ply forms two superimposed layers; a belt structure located in a radially external position with respect to the carcass structure ; a tread band located in a radially external position with respect to the belt structure ; wherein each strip-like element comprises a plurality of first cords in a side by side relationship, located in a central part of the strip-like element and each exhibiting a first average diameter (d1); wherein each of the lateral longitudinal portions of each strip-like element exhibits a reduced thickness (S2) with respect to a thickness (S1) of the central part of the strip-like element ; wherein each of the lateral longitudinal portions of each strip-like element comprises at least one second end cord with a second average diameter (d2) that is smaller than said first average diameter (d1), the respective joint exhibiting a thickness that is substantially equal to the thickness (S1) of the central part of the strip-like element ; wherein each of the lateral longitudinal portions exhibits, in a transversal section to the longitudinal development of the strip-like element , at least a connecting step between the respective lateral longitudinal portion and the central part of said strip-like element ; wherein the step is one on each longitudinal portion , the two longitudinal portions of a single strip-like element being asymmetric. <EOS>