The stability of a test equilibrium relevant to the International Thermonuclear Experimental Reactor [Fusion Eng. Des. 36, 9 (1997)] has been studied within the framework of the neoclassical island theory. The most unstable modes, with the most positive matching index Delta', have been found by solving the toroidal stability equation to have 3/2, 2/1, and 4/3 helicities. Quasilinear effects resulting from the flattening of the current profile as the island develops are important and stabilizing. Large saturated islands are predicted to arise from a combination of strong bootstrap current drive and weakly negative Delta'. The island size can be significantly reduced by applying a continuous current drive at the unstable rational surfaces. The so-obtained reduction of island width is approximately proportional to the current drive and inversely proportional to the square of the current channel. This stabilization relies on the removal of the free energy in the outer region and can thus be regarded as a Delta' effect. (C) 1999 American Institute of Physics. [S1070-664X(99)03505-3].