  Suppose the generalized Brill-Noether number is zero, we prove that there
exists a family of twice-marked smooth projective curves such that the family
of linear series with two imposed ramification conditons is irreducible.
Moreover, under certain conditions, we show that the monodromy group contains
the alternating group. In the case $r=1$, the monodromy group is the full
symmetric group.
