  We examine and explain the Luttinger-liquid character of models solvable by
the Bethe ansatz by introducing a suitable bosonic operator algebra. In the
case of the Hubbard chain, this involves two bosonic algebras which apply to
{\it all} values of $U$, electronic density, and magnetization. Only at zero
magnetization does this lead to the usual charge - spin separation. We show
that our ``pseudoparticle'' operator approach clarifies, unifies, and extends
several recent results, including the existence of independent right and left
equations of motion and the concept of ``pseudoparticle'' (also known as
``Bethe quasiparticle'').
