Pointer erratically darts over screen

[Echosyn]

I searched this and other Mac forums before posting.

Wife and I use two Mac G4s. PowerPC Digital Audio and PowerPC Mirror Door. Every day about every 2 to 10 minutes the cursor will erratically and suddenly dart across the screen to border in both computers. I have adjusted the mouse/keyboard settings several times and Universal Access is shut down. We do not use wireless hardware or devices.
Digital Audio is 80Gb, 733 MHz, and has OSX4.11
Mirror Door is 80 Gb, 1.25 GHz, and has OSX5.8

This cursor darting has been happening since we brought home the Digital Audio last January. Then last June we brought home the Mirror Door, I added a Trendnet router and LAN and the same cursor dating began in that one.
The man who sold us the computers has not heard of or
experienced this anomaly.

[SGilbert]

What brand and kind of mouse(s) are you using?