A possibility of stationary solitary electrostatic waves with large amplitude in symmetric unmagnetized symmetric pair plasmas (e(-)e(+) plasma, C60-C60+ plasma or e(-)h(+) plasma) is proven. The main idea of the work is a thermodynamic unequilibrium of plasma species which may be created in low-density ideal pair plasmas. Ranges of parameters (Mach number M and a nonequilibrium degree tau=T+/T-) which lead to the possibility of solitary waves are found. (c) 2006 American Institute of Physics.