  Within a strong coupling expansion, we construct local quasi-conserved
operators for a class of Hamiltonians that includes both integrable and
non-integrable models. We explicitly show that at the lowest orders of
perturbation theory the structure of the operators is independent of the system
details. Higher order contributions are investigated numerically by means of an
ab initio method for computing the time evolution of local operators in the
Heisenberg picture. The numerical analysis suggests that the quasi-conserved
operators could be approximations of a quasi-local conservation law, even if
the model is non-integrable.
