A magnetic resonance apparatus is operated with continuous movement of an examination subject through a measurement volume of the apparatus. At each successively-occupied position of the examination subject within the measurement volume during the continuous movement, magnetic resonance data are acquired with system parameters, each having system parameter values. Contemporaneously with each data acquisition at each position, the acquired data are evaluated as to the effect produced by the system parameter values employed to acquire the data. The system parameter values are then adapted to cause the effect to correspond to a target value, and the adapted system parameters are then used to acquire data at the next-successive position occupied by the examination subject in the continuous movement.