Why would Oldsmobile start and run, then stop and not start?

Have a 1986 Oldsmobile. Can start it, drive it, then shut it off. Try to start it again and it won't start. Could it be the fuel pump, or is there a fuel filter? How do you check for the problem? Thank you for any help.|||Sounds like a charging problem to me. Check BOTH ends of the battery cable. Replace them if corrosion has worked it's way up, under the insulation. At this age, it would be a great idea for you just to go ahead and replace them. Realize that your charging system is a 2 way street. When you start a car, power is drawn from the battery to engage the starter motor. After the car starts, the alternator and voltage regulator work together to A) recharge the battery and B) run and the engine and car electronics. Dirty cables act like resistors. They can turn the cables into a toaster if the resistance gets too high. Corrosion is the enemy here. You would be right, however, to change your fuel filter. After all these years, the filtre has probably done it's job. A dirty filter will cause you to lose top end of the vehicle (because the fuel pressure is getting obstructed). Also, the voltage of the battery is diverted partially at start up to activate the fuel pump. If there isn't enough "juice" in the battery, the fuel pump won't be working either. Good Luck!!|||i have a 88 oldsmobile and it could be dirty battery terminals or they are loose. if it was the pump or gas filter then it would,nt run as good the first time. i would be checking out the charging system first like the terminals.