  We present coalgebras of some classes of nonassociative algebras whose
associator satisfies invariance conditions given by the action of the 3-order
symmetric group. Amongst these algebras we find the well-known Vinberg
algebras, the Pre-Lie algebras, the Lie-admissible algebras and the 3-power
associative algebras. We study properties between these coalgebras and algebras
which generalize the associative case.
