Among the numerous instabilities of a plasma in a magnetic field, a prominent place is occupied by the instability that sets in when a constant electric field and a constant magnetic field are applied, and is manifest in the excitation of helical plasma-concentration waves. First discovered in semiconductor and gasdischarge plasma, it exists also in a fully ionized current-carrying plasma, and its modification exists in many plasma devices. The survey covers the main theoretical and experimental investigations of this instability, performed in gas discharges. The most complete data are available for a weakly-ionized positive column, in which the development of current-convective instability is investigated in detail in a wide range, from the limit of the onset of weak linear waves up to strong turbulence. Since it has been so thoroughly investigated, current-convective instability is used as an example to study various methods of stabilizing plasma in stabilities. These methods are the subject of Chap. 8 of the article.