This is just like the case of Russia. Geographically Russia is both Asia and Europe, so that they are eligible to participate in Asian and European events.
According to textbooks, Australia, New Zealand and many tiny small (negligible) islands are under the continent of Oceania (It's really called OCEANIA! Oceania stretches out over the Pacific and part of South East Asia, covering Australasia, Melanesia, Micronesia and Polynesia. But if you are just talking about Australia and New Zealand, you just generally call them Australasia. )
But well, Australia is accepted as part of Asia too.
There are many countries that are accepted as parts in two continents. (Like Turkey, Iran....etc)