  A finite-size scaling approach based on the transfer matrix method is
developed to calculate the critical temperature and critical exponent of the
symmetric and the asymmetric two-layer three-state Potts Models. For similar
intralayer interactions our calculation of the shift exponent $\phi $ confirm
some scaling arguments which predict $\phi = \gamma$, where $\gamma$ is the
susceptibility exponent. For unequal intralayer interactions we have obtained
$\phi = 0.5 $ which differs from the prediction $\phi = {\gamma / 2} $ of a
generalized mean-field theory.
