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A systematic investigation of electron paramagnetic resonance above the Curie temperature TC is performed on polycrystalline (La1-xYx)2/3Ca1/3MnO3 (x = 0, 0.15 and 0.2) samples. The results indicate anomalous paramagnetic behaviour below a temperature TG and, the anomalous extent increases with cooling from TG.Especially, the resonance linewidth A Hpp anomalously increases with cooling for the temperature range of TC ＜T ＜ TG. The experimental observation is discussed within the framework of the Griffiths theory that predicts the existence of ferromagnetic clusters above TC. We explain the observed anomalous paramagnetic behaviour to be due to the magnetic heterogeneity caused by the ferromagnetic clusters which appear in the Griffiths phase.