The quasiparticle current and d.c. Josepshon current in high T-C grain boun
dary junctions are calculated taking account of the brodening of the life t
ime of the quasiparticle. By properly choosing parameters, a following situ
ation is realized, where quasiparticle current has a zero bias conductance
peak, while the temperature dependence of the Josepshon current does not sh
ow any anomaly at low temperatures.