The first four chapters of Daniel occur under the rule of Babylon's king, Nebuchadnezzar. This chapter falls between his reign and when the Medo-Persians conquered in 539 BC. This chapter focuses on Belshazzar, who may have ruled Babylon concurrently with his father Nabonidus. This was probably from 553 BC until his death in 539 BC, when the city was captured. After this, Daniel serves under Darius and / or Cyrus. (BibleRef)