Meiosis requires chromosomes to line up in matched pairs before separating into gametes. A mule inherits 32 from its horse dam and 31 from its donkey sire, and the two sets differ in structure as well as number. Pairing fails for many chromosomes, the process stalls, and viable gametes are rarely produced. Male mules are effectively always sterile.
The rule has exceptions on the female side. A small number of mule mares have produced foals, with cases from China, Morocco and the United States confirmed by blood typing or genetic testing. In several instances the foal received an intact horse chromosome set from the dam, as though the donkey complement had been discarded during egg formation.
Hybrid vigour is the reason breeders persist despite sterility. Mules generally show greater endurance and hoof durability than horses of similar size and are less prone to overheating, while retaining more tractability under load than most donkeys. Every working mule must be bred afresh from its two parent species.