A rheological property of KBr partially dissolved with H2O is experimentally studied under the fixed flow rate condition. The system is a simple analogue of the partially molten asthenosphere material. When the slip rate is low, the partially moten material flows at a constant force. When the slip rate exceeds a critical value, the force starts oscillating and the amplitude of oscillation increases as a logarithmic function of the slip rate. A model is proposed to explain the irregular oscillation. It is considered that the oscillation arises because of competition between the thermodynamically stably-oriented intergranular fluid phase and the hydrodynamically stably-oriented one.