Is this an older tractor or??
Posting the Sears 917.xxxxxx # can give us a better idea of what you have.

Much of the problem is with EPA restrictions, carbs have to be set on the ragged edge of too lean.
Any type of varnish build up on the jets leans them out even more and you get a surge.
A vacuum leak can also cause the same problem.

What I'd do is examine the intake "system" to make sure all the bolts are tight.
If you don't find anything there, add a strong doseof carb cleaner to the fuel.
I prefer to do it with the tank level quite low.
Add about 10X the recommended amount and mow for an hour or so.
Top off the tank with fresh gas and run long enough to purge the fuel system of the concentrated mix.
You might get lucky.

This post was edited by bill_kapaun on Tue, Sep 17, 13 at 19:57

Thanks Bill I will check this tomorrow, It is only 3 years old, model 917289221 Briggs and Stratton Platinum 21 hp with xrd. It also has a wire that is attached to the bottom of the carb where the bowl is. I unplugged it while it was running and it stopped. Never have seen this on a carb before. I also have a DR powerwagon and this engine does the same thing, even after putting on a new carb. Have to run it on full choke to keep it running. But my main problem is this Craftsman Riding tractor. Thanks so much for your help.

The "device" on the bottom of the carb is the fuel solenoid.
It has a plunger that retracts, unblocking the Main Jet.
The purpose is to cut off fuel to the engine on shut down to prevent after fire. (back fire)

The engine is a-
Briggs 331877-1234-B1

You also need to go to the Briggs website and download a copy of the IPL for this engine.
In the IPL there is shown a "Governor link spring", item # 232, Briggs part # 691842.
If this spring is missing, there will be apparent excess play or sloppy fit in the governor linkage which can cause this kind of "hunting" as the governor tries in vain to hold the engine RPM steady under light engine loads. Engine RPM smooths out when engine load is heavy because the governor simply tries to hold the throttle plate wide open with constant pressure, so,.........no "hunting" or adjusting by the governor.

Thanks to all that are helping me on this the spring is there, I was frustrated and ended up buying a new carb, but I do not know the initial settings, I believe it is screw it in easy then back out 1/1/2 turns. Also When I got back to the rider, it would not turn over, I found out that somehow all the gas emptied into the crankcase!, Cleaned it all out, changed filter and oil twice, I ordered a shutoff gas valve for this, but never had this problem before ever. Chasing a gremlin in this darn engine. I have everything installed, New Carb, new fan, the old one had almost all the vanes missing, not sure how that happened, as it is all enclosed., new gas filter and shut off, and a new plug, oil and filter. Got everything put on, and tried to start, Now the Battery is totally dead, and will not recharge, however, I knew this was going anyway. So tomorrow I will get a Battery. It only has.4 tenths voltage. Man I guess I have a lemon here. The Dr. I put on a new Carb but something else is wrong with this, as I have to pull the plug and put gas into it to get it going, then push the primer bulb on the carb many times just to keep it running, once it gets warmed up it will stay running, but this Tecumseh Engine always was hard starting from the get go, I contacted Dr about this and they said to put in a hotter spark plug, did not change the hard starting when cold, Will let you know how I did, when I get the other battery for the Craftsman. Where I live I have to go 35 miles to get non ethanol gas, as I am finding out the gas here is messing up everyone's small engines and gas powered yard trimmers, chainsaws, etc. Thanks again for all your help it is much appreciated .

Ok, new battery, started right up ran perfect, bought the carb online from equipatron on ebay, Carb worked perfect and I am happy! Thank You for the input from my tractor friends here. now to work on that darn Tecumseh that never started easy when new. May weight until next spring for that one. Thanks again.