A method for compensating for eddy current fields in magnetic resonance images acquired using a magnetic resonance apparatus is provided. A global component of the eddy current fields corresponding to a zeroth order and a first order is compensated globally using a change in control parameters of at least one device of the magnetic resonance apparatus that is suitable for compensating for the global components (e.g., a reference oscillator and/or a gradient coil). In order to correct local higher-order eddy current fields in a volume of interest characterized by a prominent point, the residual eddy current fields remaining following compensation of the global component are developed around the point. Correction values for the control parameters are determined from the zeroth- and/or first-order local components of the development and are taken into account in the control of the magnetic resonance apparatus for magnetic resonance image acquisition.