  The nonlocality of certain quantum states can be revealed by using local
filters before performing a standard Bell test. This phenomenon, known as
hidden nonlocality, has been so far demonstrated only for a restricted class of
measurements, namely projective measurements. Here we prove the existence of
genuine hidden nonlocality. Specifically, we present a class of two-qubit
entangled states, for which we construct a local model for the most general
local measurements (POVMs), and show that the states violate a Bell inequality
after local filtering. Hence there exist entangled states, the nonlocality of
which can be revealed only by using a sequence of measurements. Finally, we
show that genuine hidden nonlocality can be maximal. There exist entangled
states for which a sequence of measurements can lead to maximal violation of a
Bell inequality, while the statistics of non-sequential measurements is always
local.
