Genesis 10 gives us a list of nations descended from Noah. At three points we are told that these nations had their own language. For example, this is Genesis 10:4-5:
Yet Genesis 11 gives us the Tower of Babel story, which tells us that God was concerned that humanity was becoming too powerful, and so decided to give humans multiple languages, where previously they had only one. This is Genesis 11:1 and Genesis 11:7:
I don't see this as a real problem, since it's not explicitly stated that the events of Genesis 11 happened after the peoples of Genesis 10 had become firmly established. In other words, Genesis 10 and 11 might not be in strict chronological order (and indeed, Genesis 11 might be intended to explain the existence of the nations mentioned in Genesis 10).