My gsx600f runs great on warm up but when its all warmed up it starts to backfire & then dies...i had carb. cleaned,replaced plugs also air cleaner & changed oil please whats next to check?

Fuel may be boiling in the line or bowl and causing a vapor lock situation .

Just some pondering........
Runs good when cold but when warms up it dies.
Have you checked for spark at the plugs right after it died?
Have you tried priming it (squirt gas into carb)
What happens if you pull the choke on the moment that it starts to die?
Wild guess? Vacuum leak at carb gasket. If bolts are not snug, when the engine warms up it might expand enough to let air in past the gasket.
Please reply as a COMMENT to this post.

Install a new spark plug

Clean or replace the air filter

Use only gas that is no more than 2 months old
& add fuel conditioner such as Sta-Bil or B&S,
unless you have to mix fuel for a 2 cycle motor

Once running & fully warm,adjust carb screws for
fuel mix at idle & fast rpm, then set the idle

Check for spark with a small engine tool avail for that
It looks like a spark plug with a clip on it & avail many places

May have to remove the carb,clean it & install a new kit,if
you still have problems

How many rpm's is it running at when you first start it up and it is running on the choke? Does it gradually start to idle back and then start to die r does it do it all of a sudden and dies?

When running with the choke on, it is on the high idle circuit of the carb, as it warms up the idle should slow down and then idle in the 800 rpm range in Park, 650 in Drive. This will be the low idle circuit range. This transition inside the carb will cover an idle air bleed hole in the venturi of the carb and lean out the mixture. If you notice that the carb smells gassy and black rich unburnt gases are coming from the tailpipe, the problem is located within the carb and requires a carb tech to do a rebuild of the carb. You could try a good carb cleaner like Lucas by putting it into the gas tank, in case you just got a bad tank of gas, but that is just a bandaid for a more deeply rooted problem. Get the carb rebuilt?

experienced similar problem (1990 1500se)-removed carbs-repaired slides-yes they can be repaired, thoroughly (replaced no carb parts) cleaned carbs-runs/idles great.

It sounds like a fuel problem. Next time it starts doing this, take the air filter cover and the air filter off. Leave the air filter backing plate on the engine and go for a ride. If it runs better, the carb is too rich. If it runs worse, the carb is too lean. They are usually jetted very lean from the factory to meet EPA standards.

If the bike is fuel injected, the dealer will have to change that as it's not owner servicable.

If you run it too long with the enricher on when it's cold, it will foul the spark plugs. The enricher is way rich. I usually only run the enricher long enough to get the warm enough to run while holding the throttle open or using the throttle lock. Don't run the enricher any longer than necessary. Put in a new set of plugs that try that. Big Twins are bad about the enricher fouling the plugs, Sportsters are the king of fouled plugs when using the enricher. When you purchase spark plugs, just buy the Autolite 4164 plugs. They run as well as anything out there and don't cost nearly as much.

Good Luck
Steve

Check your carb, fuel bowl and its float.

Replace the spark-plug, check the quality of the fuel(gas that is mixed or was stored more then three months is stale and wont fire correctly) make sure the fuel and air filter not clogged. If there is no change then your problem may be more technical, a nest may be restricting the govenor or you missed something with the carb and there still is debre causing it to stall.

Remove and clean the carbs. Clean the air filter and install new stock plugs. Re-mount the carbs and then balance and sync them. Now would also be a good time for a compression check. Valves and rings do give problems sometimes but these problems show up first as a lack of power. Since you didn't report a power problem I doubt if valves are the problem.

is this a 6cyl?
have you had the fuel pressure checked?
have you had a combustion chamber cleaning done?
have codes been read?
coolant sensor and air temp sensor checked?