What causes a car to hesitate?

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Are there particular circumstances when it hesitates? (engine hot or cold?, damp outside? certain speeds?, from a start?, etc. How many miles are on the car? Is the check engine light come on? When was the last fuel filter installed? When was the last time the throttle body was cleaned? or air induction service done? Open the hood, look at the back of the engine on the driver's side, is there oil seaping about 6 inches from the top of the engine? What did the spark plugs look like when you changed them? When were the wires last changed? Do you keep an eye on the oil level? Does it consume oil? What is the 8th digit of the vin? these answers will help.

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I remembered a site that dealt with neons, below is somthing that may help that I copied and pasted.

Common repairs: head gaskets, coils, and engine mountsThe Neon head gasket seems to typically last about 60,000 miles, at least for 1995-97 models. Calling Chrysler will usually yield a new head gasket for $100 at most, assuming you have less than 100,000 miles on your car (call 800 992 1997). The new head gasket design is better, we are told, and not likely to fail quite so quickly. Symptoms: oil in the antifreeze, oil on the engine, antifreeze in the oil. (Note that a leaking valve cover gasket can also spill oil onto the engine, though this is much less common). Dealers are also empowered to do this for free but most will not.

Chrysler did introduce a revised (MLS) head gasket which works much better and seems to be designed to last the life of the car. It was brought out in 1998 models and should have eliminated the problem - if you get a new one.

The front and rear engine mounts will tend to wear out on manual-transmission Neons, especially if they are frequently used in city traffic. The lifespan seems to be about 100,000 miles on average, much less in racing applications. These are easy to replace or repair. Some suggest adding window urethane to stiffen up the front mount, which is more appropriate for racing than daily drivers but may be handy for enthusiasts (the stiffer the mount, the smoother the shifts but the more engine vibration is transmitted into the cabin). Most people recommend the Mopar Performance replacement mounts.

Here is the site: MOPAR

Answer

check for leaking hoses such as vacuum hose. check the spark plug wires, are they connected properly, are they too old. take out all your spark plugs and check each one to see if they have enough gap at the end of it. not enough gap can cause a miss fire. do a fuel pressure check, with a fuel pressure gauge. if your car hesitates during start up, check you camshaft sensor. if you have a diesel car, check you glue plugs. its located beside spark plug