  In this paper we extend the approach of M. Cavaleri to effective amenability
to the class of computably enumerable groups, i.e. in particular we do not
assume that groups are finitely generated. In the case of computable groups we
also study complexity of the set of all effective F{\o}lner sequences and
effective paradoxical decomposition.
  In the appendix we attach a version of the paper "On decidability of
amenability in computable groups" by K. Duda and A. Ivanov which covers
Sections 9 and 10 from the previous version.
