Squealing in rear of car

My 1999 G20 has an issue with a high pitched squeal coming from the rear of the car. It only happens when the car is in motion and only for about 300 feet after the car is initially started. After that, the sound goes away for the most part. It does not seem to be related to the brakes. Could the rear axle need greasing? Any other ideas? It is very embarrassing to have such a nice vehicle do this every time I leave a location.

I had the same problem when I bought mine. The rear calipers were singed. So I had to replace the rear calipers, discs and brakes. No noise or problems since.