Relations between Egypt and Assyria were traditionally strained (to put it mildly).
The first contact between the two countries that I am aware of seems to have occurred during the Amarna Period, when an Assyrian King named Assurubalit wrote two known letters to the Egyptian Pharaoh. In one of these letters, Assurubalit says to the Pharaoh, "Gold in your country is dirt; one simply gathers it up. Why are you so sparing of it? I am engaged in building a new palace. Send me as much gold as is needed for its adornment" (Moran, William. The Amarna Letters, Baltimore: John Hopkins University Press, 1992, P. 39).
Over the next couple of centuries contact between the two countries is infrequent. In the Twenty-Fourth Dynasty Egypt fragments into a number of petty kingdoms which are conquered by the Nubians, who found the Twenty-Fifth Dynasty. The Nubian kings seemed to have been concerned about the expansion of the Assyrian Empire. As a result, they decided to send soldiers to help Hezekiah, King of Judah, against the Assyrian army, but to no avail as this seems to have only irritated Sennacherib, the Assyrian King.
Further conflicts between the two countries soon flared up. During the reign of Taharqa, the Egyptians were able to defeat an army sent by the Assyrian King Esarhadden. But only three years later, Esarhadden sent another army which successfully captured the city of Memphis (near modern Cairo). Taharqa fled south leaving his son and wife to be captured by the Assyrians (Dodson, Aidan, Afterglow of Empire, Cairo: American University in Cairo Press, p. 165).
Taharqa returned to Egypt as soon as the Assyrians left, but Esarhadden's son Ashurbanipal sent another army and once again expelled the Nubians from Egypt (Shaw, Ian. The Oxford History of Ancient Egypt, Oxford: Oxford University Press, 2000, pp. 358-9).
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