The hydrodynamic or gas-dynamic theory of plasmas including space-charge effects and several species of ions involves singular points within the plasma if the pressure and inertia of the charged particles are taken into account simultaneously. These singularities, which occur if the mean velocity of one of the species of particles reaches the sound velocity, can be removed. The required smoothing conditions lead to a well determined, non-linear eigenvalue problem for the concentrations of the various species of ions. Three methods are elaborated to calculate the eigenvalues and to obtain smooth solutions. It is shown that even under quasi-neutral conditions similar mathematical problems occur if the plasma contains several species of positive ions. The methods described can be applied to plasmas in low-pressure discharges, in hollow cathodes and near electrodes and to fusion plasmas.