1997 Sunfire wiper problem

The wipers on my 1997 Sunfire always return to the UP position - even after they are turned off. After the wipers are turned OFF, they return to their normal "down" position for a second or two, but then rotate to the "up" position (after a "click") and stop there. I tried to inspect the linkage, but was unable to remove the wiper arms - I removed the nut on each arm, but they would not budge (any help in this area would also be appreciated).