An organic electroluminescent display device includes a display that includes pixels arranged in a matrix. Each pixel includes a driver, a capacitor between a gate and a source of the driver, a switch, and a luminescent element connected to the drain of the driver. Scan lines provide a scan signal for scanning the pixels. Data lines provide a signal voltage to the pixels. Power lines are electrically connected to the source and the drain of the driver. The driver includes a back gate electrode which is provided a predetermined bias voltage. A drive circuit provides the predetermined bias voltage to the back gate electrode so that the absolute value of a threshold voltage of the driver is greater than a gate-source voltage of the driver to place the driver in a non-conducting state.