  The Bloch states of a Bose-Einstein condensates (BECs) in pure nonlinear
lattices (NLs) are dynamically unstable, so that they cannot show
superfluidity. We overcome this problem by finding that the two-component BECs
in NLs can be stabilized by the coherent linear coupling. Furthermore, in the
limit of the strong coherent coupling, the lowest Bloch band in the whole
Brillouin zone can be dynamically stable. We also find a hysteretic behavior
with loop-like structure in the Bloch band resembling the so-called
"swallowtail" loop. The dynamical stabilization and hysteretic behavior can be
observed in experiments by current technology.
