As the New Kingdom came to a close central authority once again dwindled and the next period of Egyptian history can be seen as one of disunity and is known as the Third Intermediate Period.
The period covers about 400 years, from the death of Ramesses XI through to the Assyrian conquest in 664 BCE (we’re into the realm of more solid dates by this point). At first the 21st Dynasty kings ruled in the north, and the High Priests of Amun ruled in the south – but how much this was a division of the country is debated, as there were strong links between the two power centres. During the last half of the New Kingdom Libyans had been immigrating into the Delta region, and the 22nd Dynasty arose from among these non-Egyptian people. Although the country was nominally united under the rule of a single Pharaoh for most of this time it had actually become a much looser state than it had been previously (and the 23rd Dynasty existed in parallel to parts of the 22nd Dynasty).
After the fall of the New Kingdom Nubia had once again become an independent kingdom, and the rulers of Kush took advantage of the fractured nature of Egypt at this time. They swept up north and eventually conquered and re-united the whole country under the firm rule of the 25th Dynasty. Despite this re-unification the 25th Dynasty are still seen as part of the Third Intermediate Period. They didn’t rule for very long, as they butted heads in the Levant with the rising Assyrian Empire and were eventually crushed. In 664 BCE the Assyrians sacked Memphis and Thebes, and this is considered the start of the Late Period.