Exchange bias phenomenon, evident of antiferromagnetic-ferromagnetic phase segregation state, has been observed in (Nd1-xYx)2/3Ca1/3MnO3 (x = 0, 0.1) compounds at low temperatures. A contribution to the total magnetization of the compounds due to the ferromagnetic phase has been evaluated. It has been found that yttrium doping leads to the growth of the ferromagnetic phase fraction. The ferromagnetic phase in the doped compound has a lower coercivity Hc and more rectangular form of the hysteresis loop. The values of the exchange bias field HEB and coercivity are found to be strongly dependent on the cooling magnetic field Hcool. In sufficiently high magnetic fields, Hcool > 5 kOe, HEB in the doped compound is about twice as low as in the parent compound. This difference is attributed to a lower exchange interaction and higher saturation magnetization of the ferromagnetic phase in (Nd0.9Y0.1)2/3Ca1/3MnO3.