New Zealand has no native land mammals. There are mammals that swim to new Zealand, or indeed that fly there, but all the land mammals are non native. Unfortunately with no mammals there are also no predators to control, it is also unfortunately true that in most cases introduced predators take the native flightless birds far more than the non-native mammals.
There are currently thought to be millions of wallabies living free on both of New Zealand. Finally pest control have started to try to deal with these. One pest controller can kill 100 wallabies in a good night. As elsewhere, these wallabies are causing problems, causing local plants to die and get pushed towards extinction.
It is estimated that by 2025 the cost to New Zealand could be costing $84 million a year in damaged ecosystems and lost agricultural revenue.