We study the local analytic integrability for real Liénard systems, , , with but , which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the resonant saddle into a strong saddle.