Use the word succession to describe things that follow one another, as well as the order in which they do so. The Vice President is first in line of succession to be the President and the Secretary of State is fourth.
Sometimes when a leader dies, the one who rules after him is determined not by law as in the U.S. or blood as in a monarchy but by the dying leader himself. Dictators often groom one of their sons for succession. Figuratively, you can use succession to indicate that one thing after another has come and gone without taking hold. The storefront has been home to a succession of businesses, all of which have failed. Fashions come and go in quick succession.