We analyze nonperturbatively the behavior of a Josephson junction in which
two BCS superconductors are coupled through an Anderson impurity. We recove
r earlier perturbative results which found that a delta = pi phase differen
ce is preferred when the impurity is singly occupied and the on-site Coulom
b interaction is large. We find a novel intermediate phase in which one of
delta = 0 and delta = pi is stable while the other is metastable, with the
energy E(delta) having a kink somewhere in between. As a consequence of the
kink, the I-V characteristics of the junction are modified at low voltages
. [S0031-9007(99)08784-0].