  A group G has restricted centralizers if for each g in G the centralizer
C_G(g) either is finite or has finite index in G. A theorem of Shalev states
that a profinite group with restricted centralizers is abelian-by-finite. In
the present article we handle profinite groups with restricted centralizers of
word-values. We show that if w is a multilinear commutator word and G a
profinite group with restricted centralizers of w-values, then the verbal
subgroup w(G) is abelian-by-finite.
