The Greek word (stoicheia), so translated by NRSV and REB, has puzzled commentators. It occurs at Col. 2: 8 and 20; AV renders ‘rudiments of the world’, and NJB ‘principles of this world’. The same Greek word is used by Paul in Gal. 4: 3 and 9. One view is that the word signifies the astral gods of their former religion; or perhaps the basic elements that comprise a whole, such as the letters of the alphabet; so that Paul's meaning is elementary constituents of a religious system. But more probably the ‘elemental spirits’ are the ‘angels’ of Gal. 3: 19. The Jewish belief, shared by Paul, was that the Law had been given to Israel not directly by God but through the agency of angelic powers.
Hence Christ's death, which destroyed the authority of the Law as the mediator between God and humanity, has at the same time put an end to the dominance of these angelic powers. Christ alone has supreme authority.