How long did the invasion go on before the Western Empire Fell?

Well, the invasion started after the Great Migration in 375 AD, while the Empire fell in 476 AD. Therefore, we can say that it lasted about 100 years.

Explanation:

Roman Empire was in a bad condition, when in 375 nomadic tribes from Central Asia  - Huns started the Great Migration.

Under their pressure, Germanic tribes started the invasion of the Roman Empire.

Rome was sacked in a couple of occasions, but finally fell under the attack of Ostrogoths in 476.

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