The effect of thermally activated phase slippage (TAPS) in YBa2Cu3O7 grain-boundary Josephson junctions has been studied. TAPS has been found to be responsible for the dc noise voltage superimposed on the dc Josephson current near the transition temperature. Because of the reduced Josephson coupling energy of the grain-boundary junctions, which is caused by a reduced superconducting order parameter at the grain-boundary interface, TAPS is present over a considerable temperature range. The implications of TAPS on the applicability of high-Tc Josephson junctions are outlined. © 1990 The American Physical Society.