  Given a von Neumann algebra $M$ with a faithful normal finite trace $\tau$
denote by $L^\Lambda(M, \tau)$ the generalized Arens algebra with respect to
$M.$ We give a complete description of all additive derivations on the algebra
$L^\Lambda(M, \tau).$ In particular each additive derivation on the algebra
$L^{\Lambda}(M, \tau),$ where $M$ is a type II von Neumann algebra, is inner.
