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Consider a countable amenable group acting by homeomorphisms on a compactmetrizable space. Chung and Li asked if expansiveness and positive entropy ofthe action imply existence of an off-diagonal asymptotic pair. For algebraicactions of polycyclic-by-finite groups, Chung and Li proved it does. We provideexamples showing that Chung and Li's result is near-optimal in the sense thatthe conclusion fails for some non-algebraic action generated by a singlehomeomorphism, and for some algebraic actions of non-finitely generated abeliangroups. On the other hand, we prove that every expansive action of an amenablegroup with positive entropy that has the pseudo-orbit tracing property mustadmit off-diagonal asymptotic pairs.  Using Chung and Li's algebraic characterization of expansiveness, we provethe pseudo-orbit tracing property for a class of expansive algebraic actions.This class includes every expansive principal algebraic action of an arbitrarycountable group.

Pseudo-Orbit Tracing and Algebraic actions of countable amenable groups