We present an experimental study of the effective dissipation relevant
in the thermally activated supercurrent decay of extremely underdampe
d Josephson junctions. Data referring to the supercurrent decay of Nb/
AlOx/Nb Josephson junctions are compared with the Kramers theory. Our
measurements allow us to obtain the ''effective'' resistance to be use
d in the resistively shunted junction model that results to be the sub
gap resistance due to the presence of thermally activated quasiparticl
es. The extremely low dissipation level obtained at low temperatures r
enders our result quite interesting in view of experiments in the quan
tum limit.