  The Szekeres system is studied with two methods for the determination of
conservation laws. Specifically we apply the theory of group invariant
transformations and the method of singularity analysis. We show that the
Szekeres system admits a Lagrangian and the conservation laws that we find can
be derived by the application of Noether's theorem. The stability for the
special solutions of the Szekeres system is studied and it is related with the
with the Left or Right Painlev\'e Series which describes the expansions.
