Important solar physical problems such as the heating of the corona, reconnection, and electron acceleration might be related to current-driven plasma waves, especially at low frequencies, where, perhaps, most of the wave power is concentrated. Since a direct observation of plasma waves in the solar corona is impossible, theoretical investigations are needed to clarify the possibilities of their excitation, of their nonlinear evolution, and the possible macroscopic consequences of such waves. A multifluid linear dispersion analysis of current flows parallel to the magnetic field in the solar corona is carried out. For this reason, an appropriate linear dispersion solver is developed, considering all possible propagation directions of the waves with respect to the solar magnetic field. As for the assumed plasma model, an electron distribution drifting in the direction parallel to the ambient magnetic field while the background protons were at rest was considered. Thermal effects are taken into account by means of appropriate energy equations of state. Due to their importance for the heating and anomalous transport in the solar corona, the analysis of low-frequency electrostatic waves is studied. For the limiting cases of parallel and perpendicular propagation, the Buneman and the lower-hybrid waves due to a modified two-stream instability were recovered, respectively. For realistic coronal plasma parameters of the lower corona, the dispersion curves of the two basic unstable wave modes are found to approach each other very closely, and their possible nonlinear saturation level is estimated. It appeared that for solar conditions, the two basic modes contribute a comparable (within an order of magnitude) amount of anomalous dissipation, which is quantified by estimating an “effective collision rate.”