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We study the (local) Minkowski content and the (local) fractal Eulercharacteristic of limit sets $F\subset\mathbb R$ of conformal graph directedsystems (cGDS) $\Phi$. For the local quantities we prove that the logarithmicCes\`aro averages always exist and are constant multiples of the$\delta$-conformal measure. If $\Phi$ is non-lattice, then also the non-averagelocal quantities exist and coincide with their respective average versions.When the conformal contractions of $\Phi$ are analytic, the local versionsexist if and only if $\Phi$ is non-lattice. For the non-local quantities theabove results in particular imply that limit sets of Fuchsian groups ofSchottky type are Minkowski measurable, proving a conjecture of Lapidus from1993. Further, when the contractions of the cGDS are similarities, we obtainthat the Minkowski content and the fractal Euler characteristic of $F$ exist ifand only if $\Phi$ is non-lattice, generalising earlier results by Falconer,Gatzouras, Lapidus and van Frankenhuijsen for non-degenerate self-similarsubsets of $\mathbb R$ that satisfy the open set condition.

Minkowski content and fractal Euler characteristic for conformal graph directed systems