The invention is directed toward methods for operating a series 
hybrid vehicle in a manner that responds to the operator's demand for 
power output, while maximizing 
engine efficiency and minimizing disruptions 
in vehicle drivability. According to principles of the present invention, when the driver of a series 
hybrid vehicle makes a demand for 
power output, whether the secondary power source(s) is supplied with 
secondary energy stored in an 
energy storage device(s), direct input energy generated by an engine(s), or both, depends on the amount of available 
secondary energy stored in the vehicle's secondary storage device(s) alone, and in combination with vehicle speed. During the time that the engine is used to generate 
secondary energy, the power efficiency level at which the engine is operated also depends on the vehicle speed and the amount of available secondary energy stored in the vehicle's secondary storage device alone, and in combination with vehicle speed. Further, in some embodiments, when the engine is not generating secondary energy, the engine is selectively turned off or idled in response to various operating conditions.