Moufang loops with commuting inner mappings

We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most 2. The 6-divisible Moufang loops with commuting inner mappings have nilpotency class at most 2. There is a Moufang loop of order 214 with commuting inner mappings and of nilpotency class 3.