The phase diagrams of EuFe$_{2-x}$Co$_x$As$_2$ $(0 leq x leq 0.4)$ and EuFe$_2$As$_{2-y}$P$_y$ $(0 leq y leq 0.43)$ are investigated by Eu$^{2+}$ electron spin resonance (ESR) in single crystals. From the temperature dependence of the linewidth $Delta H(T)$ of the exchange narrowed ESR line the spin-density wave (SDW) $(T < T_{rm SDW})$ and the normal metallic regime $(T > T_{rm SDW})$ are clearly distinguished. At $T > T_{rm SDW}$ the isotropic linear increase of the linewidth is driven by the Korringa relaxation which measures the conduction-electron density of states at the Fermi level. For $T < T_{rm SDW}$ the anisotropy probes the local ligand field, while the coupling to the conduction electrons disappears. With increasing substitution $x$ or $y$ the transition temperature $T_{rm SDW}$ decreases linearly accompanied by a linear decrease of the Korringa-relaxation rate from 8 Oe/K at $x=y=0$ down to 3 Oe/K at the onset of superconductivity at $x approx 0.2$ or at $y approx 0.3$, above which it remains nearly constant. Comparative ESR measurements on single crystals of the Eu diluted SDW compound Eu$_{0.2}$Sr$_{0.8}$Fe$_2$As$_2$ and superconducting (SC) Eu$_{0.22}$Sr$_{0.78}$Fe$_{1.72}$Co$_{0.28}$As$_2$ corroborate the leading influence of the ligand field on the Eu$^{2+}$ spin relaxation in the SDW regime as well as the Korringa relaxation in the normal metallic regime. Like in Eu$_{0.5}$K$_{0.5}$Fe$_2$As$_2$ a coherence peak is not detected in the latter compound at $T_{rm c}=21$ K, which is in agreement with the expected complex anisotropic SC gap structure.
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