Comments on paper by B.Lesche (Phys. Rev. E {\bf 70}, 017102 (2004))   "Renyi entropies and observables"
  It is shown that Lesche's conclusions on instability of the Renyi entropy are the same for the Tsallis entropy, as well. Moreover, they are unjustified for both entropies. 
A. G. Bashkirov