It appears the trans tries to downshift from OD to 4th for about 2-3 seconds while cruising at a steady speed, no hills, no headwind. The rpm increases 3-500 rpms then back to normal. I had my trans serviced and they say the transmission is good. I have no error codes.
Any ideas?

What size engine do you have? Were you towing or hauling anything, when this happens?

It has the 4.7 liter engine. I rarely tow anything. The symptom appears when I'm cruising at a steady speed. I even occurs when I select the tow/haul option. Sometimes it "cycles" every 15-60 seconds. This morning I noticed after I slowed to 50 mph and punched it until 80 mph, the "cycling" greatly decreased to about every 10-15 minutes.
The engine performance is good at all levels of acceleration.
Strange...........
Thanks for your interest!

It sounds like the torque converter clutch is kicking in and out for some reason. See if there is a way to disable it and see if you have the same problem.

Thank you for your reply. I give it a shot.
Not only has my Dodge ailing, my computer needed it's transmission overhauled too.