Do you know for sure that the fuel cap is venting?

tomplum is probably on the right track about the fuel tank cap vent hole being plugged up.
When the cap vent is plugged, air can't enter the tank to replace the fuel that has been consumed, so a partial vacuum develops in the tank, preventing any more fuel to leave the tank (after about 10-15 minutes run).
So the engine begins to lose power due to insufficient fuel delivery, which makes the governor react and pull the throttle plate open in an effort to restore the power (RPM) and that's when the surging begins.
Well....you wanted to know :^)

Thanks guys for the info and yes i did want to understand what was happening. I did replace the gas cap but it didn't help. I bought one of the aftermarket caps at Home Depot. When I'm using the tiller some gas, not a lot, comes out around the cap. Is this normal. It was doing this prior to changing the cap. Maybe the new cap is defective. I probably should have went to a parts store and picked up a cap. The information on this forum is great. In the past month I have replaced a chain in my craftsman rear tine tiller transmission, replaced the sump gasket in my Craftsman 3000 lawn tractor, and reworked the carbs on both of my chain saws and now this surging problem. When it rains it pours. I got the courage to tackle all this from reading the posts here. It's great to have some backup. I'm heading out to my 50th class reunion and will pick up a new cap first of the week. Thanks again.

I guess it is possible that you still have some blockage in the carb circuits.
I'm pretty sure that the compartments, and the foam/sponge material in the tank are to minimize fuel splash and subsequent leakage out the cap vent or cap threads (think: EPA mandated for reducing evaporative emissions maybe).
As this is a flat head engine, I wonder if the combustion chamber might be due for a cleaning and de-carbon service.
I also wonder if the fuel pick up tube has loosened and perhaps starts sucking air when the fuel tank level drops just a bit. This could maybe be tested by filling the tank back up to the top and see if the engine will run OK for another little while.