A criterion is presented to decide whether a produced plasma can be called a pure pair-ion plasma or not. The theory is discussed in the light of recent experiments which claim that a pure pair-ion fullerene (C-60(+/-)) plasma has been produced. It is also shown that the ion acoustic wave is replaced by the pair ion convective cell (PPCC) mode as the electron density becomes vanishingly small in a magnetized plasma comprised of positive and negative ions. The nonlinear dynamics of pure pair plasmas is described by two coupled equations which have no analog in electron-ion plasmas. In a stationary frame, it becomes similar to the Hasegawa-Mima equation but does not contain drift waves and ion acoustic waves. (c) 2007 American Institute of Physics.