The Collaborative International Dictionary of English v.0.48:

Tweedledum and Tweedledee \Twee"dle*dum` and Twee"dle*dee`\
   Two things practically alike; -- a phrase coined by John
   Byrom (1692-1793) in his satire "On the Feuds between Handel
   and Bononcini."
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

Tweedledum and Tweedledee
    n 1: any two people who are hard to tell apart [syn: Tweedledum
         and Tweedledee, Tweedledee and Tweedledum]

Moby Thesaurus II by Grady Ward, 1.0:

21 Moby Thesaurus words for "Tweedledum and Tweedledee":
   Castor and Pollux, Gemini, Siamese twins, Twin Stars, dead heat,
   deadlock, draw, even break, exact mates, fair shake,
   fraternal twins, identical twins, knotted score,
   neck-and-neck race, pair of twins, photo finish, stalemate,
   standoff, the same, tie, twins