Abstract: The headgear comprises at least one annular band for surrounding the head and possibly completed by a cap. At least the frontal-lateral part of the band includes a thick, shock-absorbent structure of resiliently-compressible foamed material. This structure is covered externally by a flexible surface layer which is resistant to abrasion and is formed as a peak having such a shape in plan as to project in correspondence with the forehead and the temporal zones to such an extent as to shield all parts of the face and any goggles respectively, from frontal blows and the ears from glancing and lateral blows.