We report low frequency noise measurements for small unshunted and shunted Nb-PbBi tunnel junctions and dc SQUIDS. We found that noise voltage spectral density varies as 1/f
α,

for all bias currents, scales accurately as V
2at high voltage levels, and depends linearly on temperature. The results show that the low frequency noise is due to fluctuations in the tunneling conductance. These fluctuations are tentatively attributed to time variations in the occupation of defect states in the barrier.