on the heels of

• upon the heels of

on the heels of

1. (idiomatic) In close pursuit of; close behind.
   • 1915, Jack London, Mutiny of the Elsinore, ch. 5:

     On the heels of the little lop-sided man appeared an overgrown dolt of a fat youth, followed by another youth.

   • 2001, Yonatan Netanyahu, The Letters of Jonathan Netanyahu, →ISBN, page 288 (Google preview):

     [T]he men got out quickly, the first ones running on the heels of those who had gotten out of the Mercedes.

2. (idiomatic, of events, facts, etc.) Closely following; in succession immediately after.
   • 1603, William Shakespeare, Hamlet, act 4, sc. 7:

     One woe doth tread upon another's heel.

   • 1643, John Milton, The Doctrine and Discipline of Divorce, book 2, ch. 4 (Google preview):

     To avoid these dreadful consequences, that tread upon the heels of those allowances to sin, will be a task of far more difficulty.

   • 1872, Mark Twain, Roughing It, ch. 77:

     [A] familiar voice chimed instantly in on the heels of my last word.

   • 1917, Upton Sinclair, King Coal, ch. 32:

     [W]hen such accidents kept happening, one on the heels of another, even the most callous public could not help asking questions.

   • 2012 Oct. 13, "Pakistan’s politics: The peace and love tour," The Economist:

     As it happened, the shooting came on the heels of a two-day “peace march” against American drone aircraft targeting suspected Islamist militants in Pakistan’s tribal areas close to the border with Afghanistan.

Commonly preceded by such verbs as follow, tread, come.

• hot on someone's heels