A steroidal nitrone of formula Ia-c, and geometric isomers E and Z thereof in double bond R 4 N =C, pharmaceutically acceptable polymorphs, salts and hydrates of said compounds, wherein R 1 independently represents a substituted or unsubstituted C 1 -C 10 alkyl radical, α-hydroxyketone, α-methylketone, or hydroxyl groups, halogen, ether with a substituted or unsubstituted C 1 -C 10 alkyl radical, primary, secondary amine with a substituted or unsubstituted C 1 -C 10 alkyl radical; tertiary amine with two substituted or unsubstituted C 1 -C 10 alkyl radicals; R 2 represents a hydrogen atom, a substituted or unsubstituted C 1 -C 10 alkyl radical, hydroxyl, halogen, ether with a substituted or unsubstituted C 1 -C 10 alkyl radical, primary, secondary amine with a substituted or unsubstituted C 1 -C 10 alkyl radical; tertiary amine with two substituted or unsubstituted C 1 -C 10 alkyl radicals, or an acyloxy group (OCOX), where X can be a substituted or unsubstituted C 1 -C 10 alkyl radical, phenyl, or an aromatic ring substituted with halogen, nitro, cyano, amino or ether groups with a substituted or unsubstituted C 1 -C 10 alkyl radical, heterocyclic pyrrole, pyridine, indole, furan, or thiophenol ring; R 3 represents a hydrogen atom, or an acyloxy group (OCOX) where X can be a substituted or unsubstitued C 1 -C 10 alkyl radical, phenyl, or an aromatic ring substituted with halogen, nitro, cyano, amino or ether groups with a substituted or unsubstitued C 1 -C 10 alkyl radical, heterocyclic pyrrole, pyridine, indole, furan, or thiophenol ring; and R 4 represents a methyl, t-butyl or benzyl group; for use in the prevention and/or treatment of cerebral stroke or ischemia, Alzheimer's disease, Parkinson's disease or amyotrophic lateral sclerosis. wherein R 1 independently represents a substituted or unsubstituted C 1 -C 10 alkyl radical, α-hydroxyketone, α-methylketone, or hydroxyl groups, halogen, ether with a substituted or unsubstituted C 1 -C 10 alkyl radical, primary, secondary amine with a substituted or unsubstituted C 1 -C 10 alkyl radical; tertiary amine with two substituted or unsubstituted C 1 -C 10 alkyl radicals; R 2 represents a hydrogen atom, a substituted or unsubstituted C 1 -C 10 alkyl radical, hydroxyl, halogen, ether with a substituted or unsubstituted C 1 -C 10 alkyl radical, primary, secondary amine with a substituted or unsubstituted C 1 -C 10 alkyl radical; tertiary amine with two substituted or unsubstituted C 1 -C 10 alkyl radicals, or an acyloxy group (OCOX), where X can be a substituted or unsubstituted C 1 -C 10 alkyl radical, phenyl, or an aromatic ring substituted with halogen, nitro, cyano, amino or ether groups with a substituted or unsubstituted C 1 -C 10 alkyl radical, heterocyclic pyrrole, pyridine, indole, furan, or thiophenol ring; R 3 represents a hydrogen atom, or an acyloxy group (OCOX) where X can be a substituted or unsubstitued C 1 -C 10 alkyl radical, phenyl, or an aromatic ring substituted with halogen, nitro, cyano, amino or ether groups with a substituted or unsubstitued C 1 -C 10 alkyl radical, heterocyclic pyrrole, pyridine, indole, furan, or thiophenol ring; and R 4 represents a methyl, t-butyl or benzyl group; for use in the prevention and/or treatment of cerebral stroke or ischemia, Alzheimer's disease, Parkinson's disease or amyotrophic lateral sclerosis.