An antenna system for a radar sensor, in particular for ascertaining distance and/or speed in the surroundings of motor vehicles, at least one part of an antenna being situated on a chip which includes at least a portion of the transceiver units of the radar sensor, and at least one second radiation-coupled part which is situated at a distance from the first part over the chip; the first part includes at least one exciter/receiver element which is part of a semiconductor element forming the chip, and the second part is a resonator element which is situated on a support and has a surface which is larger than the surface of the exciter element.