The question pertains to the biological concept of reproductive cycles in animals. The task is to identify the group of animals from the given options that do not exhibit an oestrus cycle.

The oestrus cycle is a recurring reproductive cycle found in most mammalian therian females, excluding primates, some bats, and some species of rodent. Animals that have oestrus cycles are often termed as being in 'heat' or 'in season' during their fertile period.

• Cows: Cows are known to exhibit oestrus cycles. The cycle typically includes phases such as proestrus, oestrus, metoestrus, and dioestrus.
• Rats: Similar to cows, rats also experience an oestrus cycle, which is usually very short, occurring approximately every 4 to 5 days.
• Tigers: As members of the feline family, tigers exhibit oestrus cycles as well.
• Monkeys: Unlike the other groups listed, monkeys typically exhibit a menstrual cycle instead of an oestrus cycle. This cycle includes menstruation and is similar to that seen in humans.

Conclusion: The correct answer is Monkeys, as they do not have an oestrus cycle but rather a menstrual cycle. This distinguishes them from the other listed animals, which do have oestrus cycles.