  We study Nevanlinna functions f that are transcendental meromorphic functions
having N asymptotic values and no critical values. In [KK] it was proved that
if the orbits of all the asymptotic values have accumulation sets that are
compact and on which f is a repeller, then f acts ergodically on its Julia set.
In this paper, we prove that if some, but not all of the asymptotic values have
this property, while the others are prepoles, the same holds true. This is the
first paper to consider this mixed case.
