  We analyze data on the critical current and normal state resistance noise in
Josephson junctions and argue that the noise in the critical current is due to
a mechanism that is absent in the normal state. We estimate the noise produced
by conventional Two Level Systems (TLSs) in the insulating barrier and find
that it agrees both in magnitude and in temperature dependence with the
resistance fluctuations in the normal state but it is not sufficient to explain
the critical current noise observed in large superconducting contacts. We
propose a novel microscopic mechanism for the noise in the superconducting
state in which the noise is due to electron tunneling between weak Kondo states
at subgap energies. We argue that the noise produced by this mechanism gives
temperature, area dependence and intensity that agree with the data.
