  The assumption of a new symmetry provides a nice explanation of the existence
of dark matter and an elegant way to avoid the electroweak constraints. This
symmetry often requires the pair production of new particles at colliders and
it guarantees that cascade decays down to the lightest particle give rise to
missing energy plus jets and leptons. For a long time, supersymmetry with the
conserved R-parity was the only candidate for such signals. However, any new
physics with this type of new symmetry may show up with similar signals and the
discrimination between different models at the LHC is quite challenging. In
this paper, we address the problem of discrimination between different models,
more concretely, in the little Higgs theory with T-parity (LHT) and the
supersymmetric theory with R-parity. We concentrate on the pair production of
heavy top partners, e.g., T-odd quarks in LHT and the scalar top quarks in the
MSSM at linear colliders (LC).
