The reactions of oxidative catabolism, or aerobic respiration, can occur in the mitochondrion only in the presence of

The oxidative catabolism takes place in the mitochondria, only when the process os aerobic. Thus, the presence of oxygen is required for respiration to occur in the mitochondrial matrix. 
In the absence of oxygen, the anaerobic respiration takes place, and it occurs in the cytoplasm of the cell.