The temperature dependence of electron spin resonance (ESR) was studied in EuF e2−xCoxAs2 (x = 0.0 ,0.067 ,0.1 ,0.2 ,0.25 ,0.285 ,0.35 ,0.4 and 0.5). The ESR spectrum of all the samples indicates that the g factor and peak-to-peak linewidth strongly depend on the temperature. Moreover, the peak-to-peak linewidth shows the Korringa behavior, indicating an exchange coupling between the conduction electrons and the Eu 2+ ions. The linewidth, g factor and the integrate ESR intensity show anomalies at the temperature of the spin-density-wave (SDW). The linewidth below the SDW transition does not rely on the temperature. This gives the evidence of the gap opening at the TSDW . The slope of the linewidth is closely associated to TSDW and TC. This exotic behavior may be related to the nesting of the Fermi surface.