  Palindromes are those reduced words of free products of groups that coincide
with their reverse words. We prove that a free product of groups $G$ has
infinite palindromic width, provided that $G$ is not the free product of two
cyclic groups of order two. This means that there is no a uniform bound $k$
such that every element of $G$ is a product of at most $k$ palindromes. Earlier
the similar fact established for non-abelian free groups.
