Electron-acoustic waves occur in space and laboratory plasmas where two distinct electron populations exist, namely cool and hot electrons. The observations revealed that the hot electron distribution often has a long-tailed suprathermal (non-Maxwellian) form. The aim of the present study is to investigate how various plasma parameters modify the electron-acoustic structures. We have studied the electron-acoustic waves in a collisionless and unmagnetized plasma consisting of cool inertial electrons, hot suprathermal electrons, and mobile ions. First, we started with a cold one-fluid model, and we extended it to a warm model, including the electron thermal pressure. Finally, the ion inertia was included in a two-fluid model. The linear dispersion relations for electron-acoustic waves depicted a strong dependence of the charge screening mechanism on excess suprathermality. A nonlinear (Sagdeev) pseudopotential technique was employed to investigate the existence of electron-acoustic solitary waves, and to determine how their characteristics depend on various plasma parameters. The results indicate that the thermal pressure deeply affects the electron-acoustic solitary waves. Only negative polarity waves were found to exist in the one-fluid model, which become narrower as deviation from the Maxwellian increases, while the wave amplitude at fixed soliton speed increases. However, for a constant value of the true Mach number, the amplitude decreases for increasing suprathermality. It is also found that the ion inertia has a trivial role in the supersonic domain, but it is important to support positive polarity waves in the subsonic domain., {"references":["Abbasi H., Pajouh H. H., 2007, Physics of Plasmas, 14, 012307","Armstrong T. P., Paonessa M. T., Bell E. V., II, Krimigis S. M., 1983, Journal of Geophysical Research, 88, 8893","Bale S. D., Kellogg P. 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