  We show that any Bell local state, with a hidden nonlocality that can be
revealed by local filtering, is more, or equally, entangled than nonlocal
states. More precisely, it can be deterministically transformed into a nonlocal
state, by local operations and classical communication. For such a state, there
is a clear anomaly of nonlocality, for any measures of entanglement and
nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite
state more, or equally, entangled than nonlocal states, can be revealed by
local operations and the sending of two one-bit messages, one in each
direction. For some particular states, one bit of communication is even enough.
