  Motivated by the question of which completely regular semigroups have
context-free word problem, we show that for certain classes of languages
$\mathfrak{C}$(including context-free), every completely regular semigroup that
is a union of finitely many finitely generated groups with word problem in
$\mathfrak{C}$ also has word problem in $\mathfrak{C}$. We give an example to
show that not all completely regular semigroups with context-free word problem
can be so constructed.
