I have a 1998 hyndai elantra it runs starts fine after a few minutes it cut off when i slow down or stop and will not stop for any hour or more ive put on a new fuel pump cranksenor coil pack map sens

check for vac leaks and fuel pressure

Was the car ever over heated at any time.Some friends of mine brought a elantra last summer, Where that was happening,I told them not to buy the car, But they didn,t listen to me, When i look at the car before they went end brougt it i could see antifreeze on the hood liner Where it shut out of the rad.This is a Problem with most 4 cylinder cars that i have seen. If they were Ever over heated at any time. End most of the 4 cylinder cars are bad for (Blowin)Head gaskets,Keep a eye on your temp Gauge.If it is working (Properly)

Vent valve has failed closed or cannister is clogged up. Have the evap system checked from the tank to the charcoal canister. If you need to drive to a mechanic, try driving with the gas cap loose.

problem is caused by ignition timing. your ignition timing is overly advanced.

have a mechanic check your ignition timing. adjustments in timing are done in distributor, camshaft pulley, and crackshaft pulley.

I don't have an answer for you, but I do have a similar or maybe even the same issue with mine. It usually starts up fine, and idles and runs fine when first started, however a few blocks or a few miles down the road it starts to cut out on me, sometimes dying completely... throwing it into neutral and pumping the gas usually will keep it running. This has gone on for a couple of months. When it does die, It normally will restart after sitting for a few minutes. Then a couple of weeks ago it died on me (normally this happens when slowing down and coming to a stop,) and would not restart even after a 1/2 hr, I had to have it towed. I periodically attempted to start it for over a week, it would turn over, but nothing more...then someone suggested that I disconnect the auto start box...It started right up. However, it still continues to cut out when slowing or stopping unless thrown into neutral and pumping the gas. It seems to run better on the open highway, than it does in town with all the slower speed and stop n go. I bought this car used about 6 mos. ago, and considering it's age and the 135K miles on it, I don't want to put any more money into it. I just read there is a recall on this vehicle for the fuel pump and additionally the fuel assembly, I'm not sure if this would be the answer to the whole problem or not.

my controls for the heater and air conditioner isnt working it seems like there is no power getting to the controls. ive checked fuses and they are fine, is there any power supply i can check?

possible the o2 censor but finding the right one some cars have more than one you need to know which bank and if it the front or rear sensor your local dealer should be able to tell with computer

Did you change the orfice tube(in line filter)?

check to make sure the catalytic converter is not clogged,easy way to test is remove the oxygen sensor before the converter and see if the engine still runs if so cat is probably clogged,get back to me if you need more help,please rate my fix as i strive to be the best Thanks Ray

Your car may have an "immobilizer" which is part of the security system. It will start and stall if someone uses an "unauthorized" key to start it. In other words, a key that was not programmed by Hyundai or the dealer to run the engine. This happens if you had repairs done and immobilizer was interrupted and all keys were not present for programming and you're using one of those keys perhaps and sometimes it just loses its frequency. These systems often have a different frequency each time they're coded so all keys must be programmed at the same time every time. Sometimes the immobilizer coding process is simple and included in the owners manual...NOTE: this could be an indication of a bigger problem if it keeps happening.
Good luck