  We discuss the decomposition of the zeta-determinant of the square of the
Dirac operator into contributions coming from the different parts of the
manifold. The easy case was worked in the previous paper of authors. Due to the
assumptions made on the operators in the previous paper, we were able to avoid
the presence of the small eigenvalues which provide the large time contibution
to the determinant. In the present work we analyze the general case. We offer a
detailed analysis of the contribution made by the small eigenvalues.
