An activation determining system for an oxygen sensor, comprising: an oxygen sensor configured to output a signal in accordance with an oxygen concentration in an exhaust gas from an internal combustion engine when the oxygen sensor is in an activated state; a signal processing circuit configured to receive the signal inputted thereto from the oxygen sensor, the signal processing circuit configured to output a signal in accordance with the signal inputted thereto from the oxygen sensor when the oxygen sensor is in the activated state, the signal processing circuit configured to output a signal converging to a predetermined lean output value when the oxygen sensor is in the activated state and an oxygen sensor atmosphere is maintained in the same state as the standard atmosphere, the signal processing circuit configured to output a signal converging to a predetermined convergence value different from the lean output value when the oxygen sensor is maintained in a deactivated state; and a deactivation determining section configured to determine that the oxygen sensor is in the deactivated state when the output value (Vd(n)) from the signal processing circuit falls in a predetermined deactivation range (Rna) including the convergence value; characterized in that the activation determining system further comprises a fuel supply cut-off determining section configured to determine whether or not a fuel supply cut-off in the internal combustion engine is currently executed, the deactivation determining section is configured to determine that the oxygen sensor is in the deactivated state when the output value (Vd(n)) from the signal processing circuit varies towards the convergence value for a predetermined period of time (Tth) or longer during execution of the fuel supply cut-off or when the output value (Vd(n)) from the signal processing circuit varies towards the convergence value by a predetermined amount (Vth) or greater during execution of the fuel supply cut-off. an oxygen sensor configured to output a signal in accordance with an oxygen concentration in an exhaust gas from an internal combustion engine when the oxygen sensor is in an activated state; a signal processing circuit configured to receive the signal inputted thereto from the oxygen sensor, the signal processing circuit configured to output a signal in accordance with the signal inputted thereto from the oxygen sensor when the oxygen sensor is in the activated state, the signal processing circuit configured to output a signal converging to a predetermined lean output value when the oxygen sensor is in the activated state and an oxygen sensor atmosphere is maintained in the same state as the standard atmosphere, the signal processing circuit configured to output a signal converging to a predetermined convergence value different from the lean output value when the oxygen sensor is maintained in a deactivated state; and a deactivation determining section configured to determine that the oxygen sensor is in the deactivated state when the output value (Vd(n)) from the signal processing circuit falls in a predetermined deactivation range (Rna) including the convergence value; characterized in that the activation determining system further comprises a fuel supply cut-off determining section configured to determine whether or not a fuel supply cut-off in the internal combustion engine is currently executed, the deactivation determining section is configured to determine that the oxygen sensor is in the deactivated state when the output value (Vd(n)) from the signal processing circuit varies towards the convergence value for a predetermined period of time (Tth) or longer during execution of the fuel supply cut-off or when the output value (Vd(n)) from the signal processing circuit varies towards the convergence value by a predetermined amount (Vth) or greater during execution of the fuel supply cut-off.