I have a '69 Chevelle SS and recently purchased it. I have noticed that when I step on it and let off the gas, it backfires farely often. The more gas I give it, the harder it backfires. Before I got the car, the guy who owned it before me got the car when it no longer ran. He bought a carb kit and it ran fine after that. I am presuming that the carb needs either tuning or replacement. Its a Rochester Quadrajet.

Could be a number of things, from bad timing to improperly adjusted carb to a wiped out camshaft. A Quadrajet is a somewhat difficult carb to rebuild if you are not familiar with it. I don't know if the guy who had your car was familiar with Qjets but you might want to take it to someone who has rebuilt them before. It's been my experience that an improperly rebuilt carb will not backfire, it just won't run right.

I think I would first check your timing. I would advise you to verify top dead center and make sure your harmonic balancer is correct. The outer ring on the balancer can slip and give you false readings.

And since you just bought the car and probably don't know much about the condition of the engine, it wouldn't hurt to run a compression and/or leakdown test. These can give you a very good indication as to the condition of the engine, especially the leakdown test. To check the cam, remove a valve cover and with the engine already warmed up, start the engine and watch the rocker arms to see if one might not be moving like the others. A wiped out lobe on the cam will cause a backfire. Good luck.

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-Mark "Some of us got it and some of us ain't." -Deputy Sheriff Barney Fife
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An exhaust leak ahead of the muffler/s (even a very small one that's barely audible) will cause a backfire on decelleration