  Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077
(1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two
energetically separated thresholds. The perturbation formulas for the
one-threshold case are derived as a limiting case whereby we reconstruct More's
theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error.
The perturbation formulas for the two-threshold case have additional terms due
to the non-standard orthogonality relationship of the Siegert Pseudostates. We
apply the theory to a 2-channel model problem, and find the rate of convergence
of the perturbation expansion should be examined with the aide of the variance
$D= ||E-\sum_{n}\lambda^n E^{(n)}||$ instead of the real and imaginary parts of
the perturbation energy individually.
