You can read the first such prophecy in Jeremiah 25:11-12. This prophecy was written sometime from 626 to about 586 BC and was not fulfilled until about 609 BC to 539 BC (approximately 50 years later, depending on your calculation)

"...This whole country will become a desolate wasteland, and these nations will serve the king of Babylon seventy years. But when the seventy years are fulfilled, I will punish the king of Babylon and his nation, the land of the Babylonians, for their guilt," declares the Lord, "and will make it desolate forever" (Jeremiah 25:11-12).

In this passage of Scripture, Jeremiah said that the Jews would suffer 70 years of Babylonian domination, and that after this was over, Babylon would be punished. Both parts of this prophecy were fulfilled! In 609 BC, Babylon captured the last Assyrian king and took over the holdings of the Assyrian empire, which included the land of Israel. Babylon then began to flex its muscles by taking many Jews as captives to Babylon and by destroying Jerusalem and the Temple. This domination of the Jews ended in 539 BC, when Cyrus, a leader of Persians and Medes, conquered Babylon, bringing an end to the empire. The prophecy also had another fulfilment: the Babylonians destroyed Jerusalem's Temple in 586 BC, but the Jews rebuilt it and consecrated it 70 years later, in 516 BC. Restoring the Temple showed, in a very important way, that the effects of Babylonian domination had indeed come to an end.