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Does the engine rev freely ( in neutral ) above 3000 RPM or not ? This could indicate if it is ignition or fuel related.
What kind of carb do you have ?
Vacuum secondaries or DP ?
Did you check fuel pressure and float levels ?
Do you have a fuel ( and possibly clogged ) filter ?
Does it stumble the same if you punch the throttle hard and if you do it progressively ?
What kind of distributor do you have ( points or electronic/magnetic pickup ) ?
when did you last change the plugs? I had this once, plugs looked fine but changing them solved the problem (they hadn't had much use either!).
Also check your gas tank is venting.
I was finally able to confirm my fuel starvation problem by putting the car in neutral, reving it up and holding it until it started to stumble, then shutting it off immediately and pulling my bowl sight plugs. Sure enough the primary bowl was empty and I concluded that the fuel pump was not keeping up with the engine.