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 .