  A complete classification of the complexity of the local and global
satisfiability problems for graded modal language over traditional classes of
frames have already been established. By "traditional" classes of frames, we
mean those characterized by any positive combination of reflexivity, seriality,
symmetry, transitivity, and the Euclidean property. In this paper, we fill the
gaps remaining in an analogous classification of the graded modal language with
graded converse modalities. In particular, we show its NExpTime-completeness
over the class of Euclidean frames, demonstrating this way that over this class
the considered language is harder than the language without graded modalities
or without converse modalities. We also consider its variation disallowing
graded converse modalities, but still admitting basic converse modalities. Our
most important result for this variation is confirming an earlier conjecture
that it is decidable over transitive frames. This contrasts with the
undecidability of the language with graded converse modalities.
