  We investigate the longitudinal lepton polarization asymmetry in the
exclusive processes $B\to K l^+l^-$ and $B\to K^* l^+l^-$. We include both
short and long-distance contributions to the asymmetry in our discussions. We
find that average values of the polarization asymmetries of the muon and tau
for $B\to K^{(*)}\mu^+\mu^-$ and $B\to K^{(*)}\tau^+\tau^-$ are $-0.8\ (-0.7)$
and $-0.2\ (-0.5)$, respectively.
