It was often referred to as the Dual Monarchy.
The constitutional monarchy combined the countries of Austria and Hungary in a dual monarchy. The dual monarchy came about as a result of the Compromise of 1867 made the two monarchies equal. The dual monarchy collapsed after the end of World War I.
The establishment of the Dual Monarchy in Austria
The Dual Monarchy refers to the Austria-Hungarian Empire. It is called the Dual monarchy because it was a combination of the Austrian and Hungarian Kingdoms, and their Monarchies. This came into being by the Compromise of 1867.
The Austro-Hungarian Empire, also known as Austria-Hungary, Dual Monarchy or k.u.k. Monarchy or Dual State, was a dual-monarchic union state in Central Europe from 1867 to 1918, dissolved at the end of World War I. The dual monarchy was the successor to the Austrian Empire (1804-1867) on the same territory, originating in the Austro-Hungarian Compromise of 1867 between the ruling Habsburg dynasty and the Hungarians.
Austria-Hungary was called the dual monachy.
The Austro-Hungarian Compromise of 1867 is what gave dual monarchy to Austria and Hungary. This re-established and reorganized the sovereignty of Hungary.
Whether a country is a constitutional monarchy or not does not have any bearing on the question of whether you can have dual citizenship in such a country. As a result, the answer depends on the particular country in question and its policy on dual citizenship.
The establishment of the Dual Monarchy in Austria
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Austria-Hungary
Ferenc Deak