The Babylonian War is one of the most obscure of all Hellenistic Wars. We know who it was between, roughly where it was fought, and who won, but we do not know the date or location of its decisive battle, and we can only be sure when it ended because of the future actions of the main participants.
The war was fought between Antigonus Monophthalmus, at this point the most powerful of Alexander the Great’s successors, with an empire that include most of Asia Minor and Syria, and Seleucus, satrap of Babylon since 320. At the end of the Second Diadoch War Antigonus had turned his attention to Seleucus, expelling him from Babylon. Seleucus had fled to Ptolemy in Egypt, and an alliance had formed against Antigonus.
This led to the Third Diadoch War (315-311 BC). For the first three years Seleucus had to wait impatiently in Egypt for Ptolemy to make his move. The time came in 312 BC. Ptolemy defeated Antigonus’s son Demetrius at Gaza. In the aftermath of that victory, Seleucus returned to Babylon and seized power. He then began to expand his influence in the surrounding areas, before moving into Iran.
The Third Diadoch War came to an end with the peace treaty of 311 BC. Seleucus was not included in this treaty, and Antigonus now turned his attention east, in the Babylonian War.
The actual events of the war are obscure. We know that Antigonus invaded Babylonia. He occupied part of the city of Babylon, but perhaps not the citadel, but Seleucus remained at large in the countryside. Finally there was a decisive battle, between Antigonus and (probably) Seleucus. Seleucus was victorious, and Antigonus forced to withdraw.
Seleucus’s victory was probably followed by a formal peace with Antigonus, although no details survive. In 308 Seleucus can be found campaigning on the Indian border of his empire, and Antigonus was active in the Mediterranean. Neither would have felt able to do this if there had still been an active war between them. His victory in the Babylonian War allowed Seleucus secure his control of the eastern part of Alexander’s Asian empire. This would become the foundation of the Seleucid Empire, one of the three main kingdoms of the Hellenistic age.