  The electron spin resonance absorption spectrum of Eu^{2+} ions serves as a
probe of the normal and superconducting state in Eu_{0.5}K_{0.5}Fe_2As_2. The
spin-lattice relaxation rate 1/T_1^{\rm ESR} obtained from the ESR linewidth
exhibits a Korringa-like linear increase with temperature above T_C evidencing
a normal Fermi-liquid behavior. Below 45 K deviations from the Korringa-law
occur which are ascribed to enhanced magnetic fluctuations within the FeAs
layers upon approaching the superconducting transition. Below T_C the
spin-lattice relaxation rate 1/T_1^{\rm ESR} follows a T^{1.5}-behavior without
the appearance of a coherence peak.
