In T-10 experiments, attempts were made to significantly exceed the Greenwald limit (n) over bar (Gr) during high-power (P-ab = 750 kW) electron-cyclotron resonance heating (ECRH) and gas puffing. Formally, the density limit ((n) over bar (e))(lim) exceeding the Greenwald limit (((n) over bar (e))(lim)/(n) over bar (Gr) = 1.8) was achieved for q(L) = 8.2. However, as q(L) decreased, the ratio ((n) over bar (e))(lim)/(n) over bar (Gr) also decreased, approaching unity at q(L) approximate to 3. It was suggested that the "current radius" (i.e., the radius of the magnetic surface enclosing the bulk of the plasma current I-p), rather than the limiter radius, was the parameter governing the value of ((n) over bar (e))(lim). In the ECRH experiments, no substantial degradation of plasma confinement was observed up to (n) over bar (e) similar to0.9((n) over bar (e))(lim) regardless of the ratio ((n) over bar (e))(lim)/(n) over bar (Gr). In different scenarios of the density growth up to ((n) over bar (e))(lim), two types of disruptions related to the density limit were observed. (C) 2000 MAIK "Nauka/Interperiodica".