Peroxisomal fatty acid oxidation is a metabolic process that breaks down fatty acids into smaller molecules, producing energy. The process occurs within peroxisomes, small organelles found within the cytoplasm of cells. 

These are the key steps of peroxisomal fatty acid oxidation: 

1. Fatty acids, particularly very long chain or branched fatty acids, are converted into acyl-CoA in a reaction catalyzed by an acyl-CoA oxidase isoform. During this process, hydrogen atoms are removed from the fatty acid molecule.
2. Hydrogen peroxide (H2O2) is generated as a product of fatty acid oxidation. 
3. Enzymes called catalases break down hydrogen peroxide into water and oxygen, preventing its accumulation and potential cellular damage.
4. In peroxisomes, the reaction remains incomplete, resulting in the formation of medium chain acyl-CoA, which is converted into acyl-carnitine by the carnitine octanoyl transferase enzyme. 
5. Acyl-carnitine exits the peroxisome and may be fully oxidized in the mitochondria.