Bilagrangian connections and the reduction of Lax equations

We obtain the Lax equations associated with a dynamical system endowed with a bilagrangian connection and a closed two-form parallel along the dynamical field . The case of Lagrangian dynamical systems is analysed and the nonnoether constants of motion found by Hojman and Harleston are recovered as being associated to a reduced Lax equation. Completely integrable dynamical systems are also shown to be a particular case of these systems.