In this paper, the control problems that arise during dynamic operation of a fuel-cell powered automobile, are analyzed. In particular, it is shown that there are three distinct control problems that need to be solved when the power demand fluctuates. A logic-based switching controller is proposed that switches to the battery backup when the fuel cell is unable to provide the necessary power to the motor. An adaptive controller is developed based on a linear model that adjusts the hydrogen flow into the fuel cell in response to changing power demand. Finally, a thermal controller is developed based on a nonlinear model that regulates the temperature of the fuel cell. Interaction between these controllers is analyzed via simulations under realistic road conditions.