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Let $Q$ be a tame quiver of type $\widetilde{\mathbb{A}}_n$ and $\Rep(Q)$ thecategory of finite dimensional representations over an algebraically closedfield. A representation is simply called a module. It will be shown that aregular string module has, up to isomorphism, at most two Gabriel-Roitersubmodules. The quivers $Q$ with sink-source orientations will be characterizedas those, whose central parts do not contain preinjective modules. It will alsobe shown that there are only finitely many (central) Gabriel-Roiter measuresadmitting no direct predecessors. This fact will be generalized for all tamequivers.

The Gabriel-Roiter measure for $\widetilde{\mathbb{A}}_n$ II