We show that the behavior of the excitation curves of some e^+e^- annihilation processes close to the nucleon-antinucleon threshold can be explained either by the rho(1900) resonance itself or by its interference with other resonances. Besides the six-pion annihilation and the e^+e^- -> K^+K^- pi^+pi^- and e^+e^- -> phi pi^0 processes, we also analyze the final states eta pi^+pi^-, K^+K^-pi^+pi^-pi^0, and K^+K^-pi^0pi^0, the behavior of which around 1.9 GeV has not yet attracted attention. Analysis of the data on the e^+e^- -> p (p over bar) and e^+e^- -> n (n over bar) reactions clearly shows that the rho(1900) resides above the n (n over bar) threshold.