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A parity nonconserving (PNC) asymmetry in the cross section for dielectronic recombination of polarized electrons on multiply charged ions with Z≥40 is discussed. This effect is strongly enhanced for close doubly-excited states of opposite parity in the intermediate compound ion. Such states are known for He-like ions.However, these levels have large energy and large radiative widths which hampers observation of the PNC asymmetry. We argue that accidentally degenerate states of more complex ions may be more suitable for the corresponding experiment.