  The article is showing sharpness of central limit theorems of Kipnis and
Varadhan, Derriennic and Lin, Maxwell and Woodroofe. In the case of the CLT of
Derriennic and Lin (for Markov chains with a normal operator) it is shown that
the assumption of normality cannot be relaxed. In the case of the CLT of
Maxwell and Woodroofe, the example of Peligrad and Utev is improved in the
sense of getting a convergence to different laws.
