Asmara under Italian rule was a colonial period when Eritrea's capital was ruled by the Italians. The city of Asmara came under Italian control in the 1880s after they conquered the territory of Italian Eritrea. In 1897, it was made the capital of the territory. The Italians subsequently referred to the city as "Piccola Roma".
Asmara was ruled by the Germans during World War 2.
It does not directly state that the Germans did NOT occupy or rule the city during World War 2, nor does it state that the Germans DID occupy or rule the city during World War 2.  This information is not provided.  