A helmet, especially a cricket or other sports helmet, comprises an outer shell member and, disposed adjacent its inner surface, a layer comprising an inflatable element operatively connected with inflation mechanism. The layer comprising the inflatable element preferably comprises a plurality of individual cells or pockets defined by a fluid-impermeable plastics membrane material, the individual cells or pockets being mutually in communication for pressurization and pressure-release purposes and connected to the inflation mechanism. The cells or pockets may contain impact-absorption or cushioning materials which are preferably porous to allow absorption and desorption of the inflation fluid.