  This paper is devoted to the study of unbounded derivations on Banach quasi
*-algebras with a particular emphasis to the case when they are infinitesimal
generators of one parameter automorphisms groups. Both of them, derivations and
automorphisms are considered in a weak sense; i.e., with the use of a certain
families of bounded sesquilinear forms. Conditions for a weak *-derivation to
be the generator of a *-automorphisms group are given.
