  The non-mesonic weak decay of $\Lambda$--hypernuclei is studied within a
one-meson-exchange potential supplemented by a chirally motivated
two-pion-exchange mechanism. The effects of final state interactions on the
outgoing nucleons are also taken into account. In view of the severe
discrepancies between theoretical expectations and experimental data,
particular attention is payed to the asymmetry of the protons emitted by
polarized hypernuclei. The one-meson-exchange model describes the non-mesonic
rates and the neutron-to-proton ratio satisfactorily but predicts a too large
and negative asymmetry parameter. The uncorrelated and correlated two-pion
mechanisms change the rates moderately, thus maintaining the agreement with
experiment. The modification in the strength and sign of some decay amplitudes
becomes crucial and produces asymmetry parameters which lie well within the
experimental observations.
