  We study balancedness properties of words given by the Arnoux-Rauzy and Brun
multi-dimensional continued fraction algorithms. We show that almost all Brun
words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely
balanced; in particular, boundedness of the strong partial quotients implies
balancedness. On the other hand, we provide examples of unbalanced Brun words
on 3 letters.
