Headwear having a crown and a headband attached to and extending around the lower inside edge of the crown. A visor part may also be attached to the underside of the crown. The headband is made of two sheets of elastic cloth excluding polyurethane yarn so as to provide good stretch without imposing undue elastic pressure on the wearer. The crown is made of several sheets of material, at least two of which are attached to each other by an elastic connecting portion for increased stretch and wearer comfort.