I am skeptical that these hydrogen/oxygen generators give you more mileage, but I did see one interesting theory on why they might work on the web somewhere:

The theory is that the small amount of hydrogen/oxygen introduced into each cylinder was able to make the flame front burn much faster than a gasoline/air mixture, and therefore you could move the timing so that the spark happened much closer to TDC, thus making the engine more efficient. In other words, more of the power of the mixture burning was transferred into the crankshaft. This version of the theory doesn't try to claim that you get any additional energy from the Hydrogen/Oxygen that was put into the cylinder, only that the flame speed makes the engine more efficient.

Does anyone have any information or comments on this?