The relative occupation of competing states of local stability is not determined solely by the characteristics of the locally favored states, but depends on the noise along the whole path connecting the competing states. This is not new, but the sophistication of most modern treatments has obscured the simplicity of this central point, and here it is argued for in simple physical terms. In addition, recent work by van Kampen and by Büttiker, for particles in closed loops, subject to a force field, heavy damping, and a temperature which is a function of position in the loop, are supplemented. In that case, circulating currents are set up, and these are evaluated. A final speculative section emphasizes the difficulty in calculating the long-term time evolution of the probability distribution in complex multistable systems with state-dependent noise. © 1988 Plenum Publishing Corporation.