The invention relates to a drug combination including xenon gas and at least one antioxidant, in liquid or solid form, for use in treating, slowing, or preventing neurological damage following a neurodegenerative disease in a human being. Preferably, the xenon content is 10% to 80% by volume. Also, the antioxidant is preferably vitamin E, a vitamin E analog, or a vitamin E derivative. The neurodegenerative disease is Parkinsons disease or a disease related to Parkinsons disease.