In NSW we have Australia's oldest National Park (and the 2nd oldest National Park in the world), the "Royal National Park", however - it is a State park, not a Commonwealth park. It was proclaimed National Park in 1879 before Australia was proclaimed in 1901 but has never been "downgraded" or renamed to a "mere" State Park.
The Lane Cove National Park was proclaimed in 1938 by the State Government.
How do YOU know the Yanks aren't as careless with their nomenclature as we are?
