Thanks Juleous. I didn't explain well but the heat/cool switch will shut the a/c off and then switch it to run the furnace non-stop if allowed to do so. I'm not familiar with what the contactor looks like and where it is at, inside the furnace&a/c or inside the condensing unit outside? Is that like the points in the voltage regulator on my old 50 chevy where I would rap on the cover with a screwdriver to unstick them? Any voltmeter or ammeter test you would suggest?
Sorry I didn't understand I guess what your problem is. Is the fan in the furnace the part that runs all the time, or is it the condensing unit outside. And yes the contactor is like the points on your old car and they are located in the condensing unit outside under the cover panel.
I went over tonight with a new thermostat and that didn't fix it. The old one was ok. Switch it to heat and the heat ran all the time. Switched it back and the ac ran all the time. Yes fan blower and condensing unit ran together except on heat and then only the blower ran. Checked by the compressor and bumped the contactor points with a screwdriver and it shut off. Sprayed the part that slides with wd40 and that has fixed it, so far anyway. I'm not sure why switching to heat would shut off the condensing unit even with the points still stuck. Thanks for your help.
It won't if the contacts are stuck it should never turn off no matter what you do? I think you need to call someone I can't help you much from here.
The t-stat may be miswired. Make sure that the cooling wire,,(yel or blue) is on the "Y" terminal and Heating wire is on the "W" terminal. If you have the cooling wire on "o" terminal it will run all the time. If heat wire is on "b" the same thing. I will check back tomarrow to see if you have solved the problem....
After reading all the replies, you must have a heat pump....Great call Juleous!!!!! 

[This message has been edited by HOLLYWOOD (edited July 12, 2000).]
Sorry Hollywood, been gone for a while. It isn't a heat pump. I replaced the sequencer and that appears to have fixed it. The sequencer being a relay by the heat/cool switch. Thanks guys.
I'm having the same problem, I have a heat pump and when the furnaces turns off the unit outside keeps running. Could someone help me out?
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Air Conditioning:
Had my wine cellar cooling/ humidifying system replace. Smith got me estimates from Jim Gallagher and his partner Vince and they were great. They are incredibly responsive, professional, friendly and reliable. We had 3 other wine cellar specialist who dropped the ball in one way or another ,not returning calls. But Through Smith it help me a lot . Check out http://goo.gl/UMfeoI