  We present period-luminosity relations for more than 3,200 red variable stars
in the Small Magellanic Cloud observed in the second phase of the Optical
Gravitational Lensing Experiment (OGLE-II). Periods of multiply-periodic light
curve solutions combined with the single-epoch 2MASS JHK_S magnitudes, reveal
very similar distributions to those for the Large Magellanic Cloud in Paper I.
The main features include four pulsating Asymptotic Giant Branch (AGB) ridges,
three distinct short-period sequences below the tip of the Red Giant Branch and
two long-period sequences of ambiguous origin. We derive a relative distance
modulus of the Clouds from the period-luminosity distributions for all stars of
Delta mu_0=0.44 mag, which is in good agreement with recent independent
results. The tip of the Red Giant Branch shows a colour and metallicity
dependence that is in excellent agreement with the empirical results for
globular clusters. We conclude that most variable stars below the TRGB are
indeed RGB stars.
