We perform a systematic study of the time evolution of the transport critic
al current in polycrystalline samples of the high temperature superconducti
ng system (Hg1-xRex)Ba2Ca2Cu3O8+delta and YBa2Cu3O7-delta after application
and removal of an external magnetic field H-m. Within our time, temperatur
e, and remanent field windows, the transport critical current increases log
arithmically in time. The relaxation rates in the range 80-115 K decrease w
ith increasing temperature at a fixed H-m, while temperature-dependent maxi
ma are observed in the relaxation rate versus H-m, plots. These experimenta
l results are reproduced by a phenomenological model applicable to any high
-T-c, polycrystals. In the model, the time increase of the transport curren
t is determined by the effective field at the intergrain junctions, which r
elaxes in time due to the flux creep of the intragrain magnetization. [S016
3-1829(99)00729-8].