The present disclosure provides novel methods for treating or preventing amyotrophic lateral sclerosis (ALS), methods for delaying the onset of neurological symptoms associated with ALS, increasing survival in subjects afflicted with ALS, and attenuating the decline of muscle strength associated with ALS in a subject in need thereof. The present disclosure also provides methods for treating or preventing α-synucleinopathy or TDP-43 proteinopathy. The methods comprise administering to the subject an effective amount of a mitochondria-targeting peptidomimetic compound, such as (R)-2-amino-N—((S)-1-(((S)-5-amino-1-(3-benzyl-1,2,4-oxadiazol-5-yl)pentyl)amino)-3-(4-hydroxy-2,6-dimethylphenyl)-1-oxopropan-2-yl)-5-guanidinopentanamide, or a pharmaceutically acceptable salt, stereoisomer, tautomer, hydrate, and/or solvate thereof.