[en] A method of approximate analytical evaluation of ionic off-resonance terms in the dispersion equation for ion-cyclotron waves, appropriate for lower-order harmonics (≤3) and for T_e/T_i ≤10, is presented. The significance of these terms for the quasi-perpendicular electrostatic ion-cyclotron modes and instabilities in the longwave range (modal wavelengths larger than the electron mean free path), in a weakly-ionized Maxwellian plasma with one and two ion species and with electrons drifting along magnetic lines of force (e.g. low-temperature, low-pressure gas discharges, astro-geophysical situations), is demonstrated. It is shown that the inclusion of the off-resonance terms alters the forms of spectra, lowers the threshold drifts and augments the critical wavelengths at which the instabilities set in. Moreover, for some values of T_e/T_i the order of excitation of harmonics is reversed, as the second harmonic is found to have a smaller threshold drift than the first one. (author)