Model is 917.270810.

"Hi Test" gasoline is a total waste of money in your engine. In fact, it will be negligibly less efficient.

So-
The symptom occurs when you go to "put it up".
Just what does that entail?
Possibly running out of fuel?

If you are referring to the engine RPM increasing and decreasing in regular, rapid cycles after you disengage the mower deck and are not actually driving........you are only observing the action of the engine speed governor as it "hunts" for the sweet spot of governed RPM without the load of the mower deck or the transmission to help "dampen" the surges.
When the deck is engaged, or you are driving, the engine is under some load and can't surge because the load factor keeps the engine from speeding up rapidly, and slowing down rapidly..........thus the governor can find and hold its sweet spot of governed RPM without having to constantly adjust.
Without any external loading on the engine, the RPMs can change very rapidly and this causes the governor to try and adjust the RPM to the governed speed but it usually turns into a game of OVER COMPENSATION in both higher and lower RPM fluctuations.
This is not a harmful condition, if this is what you are hearing.
These old Opp Twins have a tendency to do this as they accumulate some age and wear.
I would not give it a second thought.
And what Bill said about "High Test" gasoline is true. This is one of the most persistent myths in automotive gossip that "Premium Grade" fuel is better for ailing engines.
Truth is, unless your engine has a very high compression ratio, you will not gain a thing by paying the higher price.
High Test actually burns slower and is more difficult to ignite, than regular grade gasoline, when burned in a standard, low compression engine.
It is only by virtue of a higher compression engine that the extra power potential of High Test gasoline can be realized.
Put High Test in a standard engine and the actual power output drops slightly, because a good portion of each fuel charge that goes into the cylinder, goes right on out the exhaust...........unburned.

A vacuum leak can also cause surging.
Check the intake mounting bolts etc.

Possibly a strong dose of carb cleaner may fix things, if the Jet's have gum/varnish build up.

Thanks for the input. I only used HT because it was suggested by the local dealer to cut down on effects from Ethanol in the fuel. Obviously BS. I never thought that it would increase power I am well aware of the types of gas in autos, but figured the dealer (not SEARS) in his repair experience of small engines and two cycles might know better. I will now discipline my self to drain and clean the gasoline from these small engines at the end of the season and start and run them during the season. At any rate I will clean the carb with cleaner and check for any vacuum leaks and post the results later today.

Hi octane gas can be useful in high performance 2 stroke engines such as chain saws.
For the more mundane 4 stroke engines, that's not the case.
Octane rating is simply a degree of resistance to detonation.
Even on a high compression engine, that typically doesn't occur until you open the throttle wide so that the cylinder can get a full "gulp" of air.

OK...changed the vac line and sprayed carb cleaner, helped a little. Power surge may be the wrong term. The engine is hunting for the right RPM as mentioned above, but can be now made to run by using some choke. It will hunt under load until I find the right amount of choke. I may have carried the HT over to the 4 strokes because the dealer was fixing a chain saw and a lawn mower and he could only have meant the chain saw. Could this problem be caused by water in the gas ( I have removed latest and refreshed), but still needs some chock.