  Neutrino physics is nowadays receiving more and more attention as a possible
source of information for the long-standing problem of new physics beyond the
Standard Model. The recent measurement of the third mixing angle theta13 in the
standard mixing oscillation scenario encourages us to pursue the still missing
results on leptonic CP violation and absolute neutrino masses. However, several
puzzling measurements exist, which deserve an exhaustive evaluation. The NESSiE
Collaboration has been setup to undertake a definitive experiment to clarify
the muon disappearance measurements at small L/E, which will be able to put
severe constraints to any model with more than the three-standard neutrinos, or
even to robustly measure the presence of a new kind of neutrino oscillation for
the first time. Within the context of the current CERN project, aimed to
revitalize the neutrino field in Europe, we will illustrate the achievements
that can be obtained by a double muon-spectrometer system, with emphasis on the
search for sterile neutrinos.
