An internal multi-band antenna and a radio device comprising such an antenna. A radiator (320) of the antenna is a conductivepart of the outer cover (COV) of a radio device or conductive coating of the cover. The radiator is electromagnetically fed by a feed element (330) which is isolated from the radiator by a relatively thin dielectric layer. The feed element is shaped so that it has, together with the other parts of the antenna, resonance frequencies in the range of at least two desired operating bands. The antenna structure further includes a parasitic tuning element (340) and a switch (SW) by which the tuning element can be coupled to the signal ground (GND) through at least two alternative reactive circuits. The tuning element is dimensioned and placed and the component values of the reactive circuits are chosen so that of two operating bands of the antenna the locations of both are displaced in a desired way when changing the state of the switch. By means of a relatively simple switch arrangement, the antenna can be made to cover the frequency ranges of four systems, and it can also be optimised for each system separately, because its operating bands only cover the range used by one system at a time.