  We construct two infinite series of Moufang loops of exponent $3$ whose
commutative center (i.e. the set of elements that commute with all elements of
the loop) is not a normal subloop. In particular, we obtain examples of such
loops of orders $3^8$ and $3^{11}$ one of which can be defined as the Moufang
triplication of the free Burnside group $B(3,3)$.
