Egypt had many centuries of relative peace with occasional periods of disturbance, but nothing like the chaos of Mesopotamia. After a period of time in the second millennium B.C.E. two peoples began to assume dominance, the Babylonians who had been culturally dominant for many centuries in the south, and the Assyrians in the north. As it turned out, while both groups were politically dominant at times, in general it can be said that the Assyrians were more often politically dominant while the Babylonians were culturally dominant. In fact the Assyrians even used the Babylonian dialect of Akkadian for their own official records. Here are some dates in Mesopotamian history from this point on.
All dates assume that something like the modern system of chronology.
Even in modern sources these dates vary. B.C.E. Hammurabi unifies the area around Babylon. The rise of the Assyrian Empire. 730-650 B.C.E. Assyrian Empire controls all of Mesopotamia, parts of Persia, Syria, Palestine, and Egypt. This is also notable as the first time that Egypt and Babylon were under the same regime.