  We analyse the muon longitudinal polarization asymmetry \Delta_long in the
decay K^+ --> \pi^+ \mu^+ mu^-. It is stressed that, since the muon helicities
are not Lorentz-invariant quantities, the magnitude of \Delta_long depends in
general on the reference frame. We consider the muon helicities in the LAB
system, and study the sensitivity of the longitudinal polarization asymmetry to
the flavour-mixing parameters in the Standard Model for stopped and in-flight
decaying K^+. A similar analysis is carried out for the decay K_L --> \mu^+
\mu^-. We find that in both cases the asymmetry is diluted when increasing the
energy of the decaying kaons.
