The dynamics of an almost symmetrical double-well system coupled to an Ohmic heat bath is studied. This case is of potential relevance to the problem of quantum coherence in SQUID rings. The coherent quantum oscillations characteristic for isolated systems are shown to be strongly affected by dissipation. We report on recent analytical results describing the influence of thermal fluctuation and biasing forces. The range of parameters in which quantum coherence survives is determined and the time evolution of the occupation probabilities in the two wells is calculated.