1998 Honda Accord Check Engine Light

Over the past 8 months our check engine light has been on repeatedly and almost continuously. We've taken the car to our mechanic, who has replaced two destroyed catalytic converters, cleaned the EGR valve 3 times and who tells us there are black soot-like deposits in the system. The most recently destroyed cat, he said, was vaporized inside in a very short time period. Does anyone have any idea what might cause such troubles? Have any other Accord owners experienced anything similar? I'm wondering if the onboard computer might be causing some sort of fuel mixture problem resulting in black soot that is destroying the cats and gunking up the EGR valve. I'm desperate for an answer - the car is otherwise a great car with lots of years left.