What are some similarities between the governments of the United States and Australia?

The major similarity between these two governments is that
both of them are constitutional federal democracies.  In addition, both have some degree
of separation of powers.

Both countries have written
constitutions that are the supreme law of the land.  In both cases, the constitutions
give some powers to the states that cannot be taken away by the federal government
unless the constitution is amended.  Both countries' laws are made by elected
legislatures that have two houses.  In both countries, laws made by the elected
legislatures may be overturned by courts if the laws are found to be
unconstitutional.

Thus, the two countries have very similar
systems.  There are major differences, but they are less important than the fact that
both countries are constitutional federal democracies.