SYDNEY—One of the few bright spots in real estate amid a three-year global slump, Australia now faces falling home prices and fears of overbuilding.

A downturn in Australia's real estate market will add to concerns of a two-speed economy in the resource-rich nation. Mining profits are surging due to heavy demand from China and other fast-growing Asian countries, but consumer businesses and manufacturing have faltered under the weight of the swollen Australian dollar, which is trading near 30-year highs to the U.S. currency.

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