Abstract
We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then we prove the completeness of the system of transversal components of eigenwaves and associated waves as well as the `minimality' of this system and show that this system is generally not a Schauder basis.
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