  We calculate a number of observables related to particle-antiparticle mixing
in the Littlest Higgs model with T-parity (LHT). The resulting effective
Hamiltonian for Delta F=2 transitions agrees with the one of Hubisz et al., but
our phenomenological analysis goes far beyond the one of these authors. In
particular, we point out that the presence of mirror fermions with new flavour
and CP-violating interactions allows to remove the possible Standard Model (SM)
discrepancy between the CP asymmetry S_{psi K_S} and large values of |V_ub| and
to obtain for the mass difference Delta M_s < (Delta M_s)_SM as suggested by
the recent result by the CDF collaboration. We also identify a scenario in
which simultaneously significant enhancements of the CP asymmetries S_{phi psi}
and A_SL^q relative to the SM are possible, while satisfying all existing
constraints, in particular from the B -> X_s gamma decay and A_CP(B -> X_s
gamma) that are presented in the LHT model here for the first time. In another
scenario the second, non-SM, value for the angle gamma=-(109+-6) from tree
level decays, although unlikely, can be made consistent with all existing data
with the help of mirror fermions. We present a number of correlations between
the observables in question and study the implications of our results for the
mass spectrum and the weak mixing matrix of mirror fermions. In the most
interesting scenarios, the latter one turns out to have a hierarchical
structure that differs significantly from the CKM one.
