The paper discusses the dispersion relation for longitudinal electron waves propagating in a collisionless, homogeneous isotropic plasma, which contains both Maxwellian and suprathermal electrons. It is found that the dispersion curve, known to have two separate branches for zero suprathermal energy spread, depends sensitively on this quantity. As the energy half-width of the suprathermal population increases, the branches approach each other until they touch at a connexion point, for a small critical value of that half-width. The topology of the dispersion curves is different for half-widths above and below critical; and this can affect the use of wave-propagation measurements as a diagnostic technique for the determination of the electron distribution function. Both the distance between the branches and spatial damping near the connexion frequency depend on the half-width, if below critical, and can be used to determine it. The theory is applied to experimental data.