  Basic definitions and properties of nearly associative algebras are
described. Nearly associative algebras are proved to be Lie-admissible
algebras. Two-dimensional nearly associative algebras are classified, and its
main classes are derived. The bimodules, matched pairs and Manin triple of a
nearly associative algebras are derived and their equivalence with nearly
associative bialgebras is proved. Basic definitions and properties of nearly
Hom-associative algebras are described. Related bimodules and matched pairs are
given, and associated identities are established.
