A local antenna for transmitting and/or receiving radio frequency signals in a nuclear magnetic resonance imaging apparatus includes first and second sub-antennas which are axially spaced from each other. The sub-antennas each are composed of at least one conductor turn. An electrical series circuit is formed of the first sub-antenna, a capacitive element for shortening the path length effective for the radio frequency signal and of the second sub-antenna. The two sub-antennas have the same winding direction. A capacitor is connected in parallel with the series circuit. The respective capacitance values of the series capacitive element and the parallel capacitor are approximately the same. For constructing a local antenna system especially suitable for mammography, two such local antennas are arranged side-by-side and are electrically connected in parallel. The series capacitive elements of the two local antennas face each other.