We report the observation of an unusual electron spin resonance (ESR) signal in single crystals of Eu2CuO4. The signal appears to be associated with a resonance mode of the CuO2 planes, similar to the midfield and low-field absorptions we have reported previously [Phys. Rev. B 41, 1934 (1990)]. However, it is only observed when the projection of the applied dc magnetic field in the CuO2 plane is within a few degrees of the 〈110〉 crystallographic direction. Additionally the sample must be field cooled in the CuO2 plane, but with a component of the cooling field perpendicular to the 〈110〉 ESR observation direction. Both the field for resonance and the linewidth exhibit a 1/cos θ dependence, where θ is the angle of the applied dc field between the c axis and the 〈110〉 observation direction. Additional constraints for observation of the resonance are that the microwave rf magnetic field must have a component in the CuO2 plane, but perpendicular to the dc field. The signal disappears above ∼215 K, which we assume is associated with the antiferromagnetic ordering temperature
