The authors report the observation of a Griffiths-like phase in La2−2xSr1+2xMn2O7 (x = 0.30, 0.33, and 0.40) and (La0.8Eu0.2)2−2xSr1+2xMn2O7 (x = 0.33) single crystals by means of electron spin resonance, magnetic susceptibility, and magnetoresistance measurements. In the temperature region TC<T<350 K, the resonance signal consists of a ferromagnetic resonance line and a paramagnetic resonance line, which suggests that the system is not in a pure paramagnetic phase. The ferromagnetic resonance signal disappears and the magnetic susceptibility starts to deviate from the Curie-Weiss law at the same temperature T* ≈ 350 K, independent of doping level and anisotropy. These results indicate that a Griffiths-like phase exists at TC<T<T* in bilayered manganites, which is due to intrinsic inhomogeneity caused by quenched disorder.