A nuclear magnetic resonance tomography apparatus has gradient coils that superimpose at least one gradient field on a basic magnetic field transversely to a coding direction, with an overall magnetic field in the coding direction having a magnetic field strength with a component that changes quadratically over distance. A support mechanism displaces a subject to be measured by a distance .DELTA.w in the coding direction, and a control computer determines an absolute location w of a nuclear magnetic resonance signal in the coding direction from the resulting, quadratically dependent phase differences or resonant frequency differences during the displacement of the subject.