The present invention relates to compounds of Formula I, IA, II, HA, III, orIHA and their pharmaceutical uses.Particular aspects of the invention relate to the use of those compounds forthe selective inhibition of one or more caspases. Alsodescribed are methods where the compounds of Formula I, IA, II, IIA, III, orIIIA are used in the prevention and/or treatment ofvarious diseases and conditions in subjects, including caspase-mediateddiseases such as sepsis, myocardial infarction, ischemicstroke, spinal cord injury (SCI), traumatic brain injury (TBI) andneurodegenerative disease (e.g. multiple sclerosis (MS) andAlzheimer's, Parkinson's, and Huntington's diseases).