This invention relates to a Start-Stop method for a heavy-duty hybrid vehicle that turns off the internal combustion engine when the vehicle stops or, optionally, when the vehicle travels downhill. The Stop-Start method automatically restarts the internal combustion engine when the vehicle starts accelerating or is no longer traveling downhill. The software instructions for the Stop-Start method reside within the programming of the hybrid vehicle control computer as a subset of the hybrid vehicle control strategy in hybrid-electric or hybrid-hydraulic heavy-duty vehicle. During the time the internal combustion engine is turned off the necessary vehicle accessories operate from the available power of the hybrid high power energy storage.