The current-voltage characteristics of Josephson tunnel junctions shunted by a resistance with a substantial self-inductance exhibit stable negative-resistance regions. Very large increases in the low-frequency voltage noise with temperatures of 106 K or more observed near these regions arise from switching between subharmonic modes. Moderate increases in the noise, with temperatures of about 103 K, arise from chaotic behavior. These results are substantiated by analog and digital simulations. © 1983 The American Physical Society.