The superfluidity of Bose-Einstein condensates (BECs) in optical lattices i
s investigated. Apart from the usual Landau instability, which occurs when
a BEC flows faster than the speed of sound, the BEC can also suffer a dynam
ical instability, resulting in period doubling and other sorts of symmetry
breaking of the system. Such an instability plays a crucial role in the dis
sipative motion of a trapped BEC in an optical lattice recently observed.