The Slavs as a linguistic group didn't arrive in the Balkans until the migration period of the 6th century. Around the same time, the region was also invaded by the Turkic Bulgars, who were gradually Slavicised until all that was left was the name. As to who dominated the Balkans before, the answer is Rome, who ruled the region from around 20 CE until the arrival of the Slavs and Bulgars. The Adriatic coast had been a Roman province for much longer than that, and Emperor Diocletian's palace forms the center of the Croatian city of Split. Before that, the eastern portions, which are now Macedonia and Bulgaria, where ruled by the Persians for a time and subsequently the Greeks.

However, the answer to who the dominant population was in the Balkans is very different. In the east, the main groups where the Thracians and the Dacians, who had frequent contact with the Greeks to the south, but spoke a very different language and tended to no organize politically on a large scale. The western Balkans were inhabited by the Illyrians, of who not much is actually known. We know that they were never united as one "Illyrian" cultural group, and that the place known as Illyria by the Greeks and Romans was inhabited by numerous tribes who didn't necessarily have a lot in common. Some of them where influenced by Celtic cultures from northern Italy and modern day Austria. Occasionally, one group would rise to become particularly powerful, but no one dominated the whole region politically.