Anomalies in the magnetization and crystal dilatation have been observed in the mixed state of UPd2Al3 and CeRu2. To explain the anomalies we study a superconducting system with large spin susceptibility. We predict a new superconducting state in which the superconducting order parameter has a periodic array of planar nodes perpendicular to the vortices. The nature of this generalized Fulde-Ferrell-Larkin-Ovchinnikov state is discussed in connection with the peak effect in the magnetization process of UPd2Al3 and CeRu2.