The Austro-Hungarian empire (as such) only existed from 1867 to 1918.

During that period it fought two wars that might be considered colonial (or imperial, depending on definitions).

In 1878, the Empire seized Boznia and Herzegovina from the Ottoman Empire.

From 1899 to 1901, Austria-Hungary participated in the Boxer Rebellion in China, in conjunction with allies: France, Germany, Italy, Japan, Russia, the United Kingdom, the United States.

Before the Austro-Hungarian Empire was formed, the Austrian Empire and the Archduchy of Austria fought in other wars which might (or might not) be considered "colonial".