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As revealed by the observation of memory effects and domain imaging, the antiferromagnetic (AFM) spin structure in exchange bias is not static. During reversal, the AFM spins form an exchange spring connected with the ferromagnet (FM). We have observed hybrid domain walls consisting of FM and AFM sections and their evolution using the magnetooptical indicator film technique. The external magnetic field moves only the FM section of the hybrid domain walls, leading to the formation of an exchange spring parallel to the interface. The nucleation and unwinding of the exchange spring occur at different locations, and the propagation depends strongly on the chirality of the FM domain walls.