Fluctuations can play an important role in determining the behavior of Josephson junctions when the coupling energy across the junction is the order of thermal energies. This situation can be realized near the critical temperature and near the minima of the I1(H) curve at low temperatures. In these regimes the effects of thermal fluctuations on the I-V characteristic are quite dramatic. Using a carefully shielded, thermally-regulated apparatus we have measured I⇔-V characteristic of an almost ideal Josephson junction in both of these regimes. The results are in qualitative agreement with calculations which treat the problem of thermal fluctuations in a junction using an analogy with the Brownian motion of a particle in a field of force.