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A simple closed curve $\alpha$ in the boundary of a genus two handlebody $H$is primitive if adding a 2-handle to $H$ along $\alpha$ yields a solid torus.If adding a 2-handle to $H$ along $\alpha$ yields a Seifert-fibered space andnot a solid torus, the curve is called Seifert. If $\alpha$ is disjoint from anessential separating disk in $H$, does not bound a disk in $H$, and is notprimitive in $H$, then it is said to be proper power.  As one of the background papers of the classification project of hyperbolicprimitive/Seifert knots in $S^3$ whose complete list is given in [BK20], thispaper classifies in terms of R-R diagrams primitive, proper power, and Seifertcurves. In other words, we provide up to equivalence all possible R-R diagramsof such curves. Furthermore, we further classify all possible R-R diagrams ofproper power curves with respect to an arbitrary complete set of cutting disksof a genus two handlebody.

Primitive, proper power, and Seifert curves in the boundary of a genus two handlebody