Apologies in advance if this is like asking for help tying my shoelaces...

I have Premiere 6.5.

The edit line in the time line moves off the page to the right when I am looking at the 1 second view, for example.

Is there any way to keep the edit line still and the timeline scrolling?

Or if the edit line must scroll, when it reaches the far right, can the timeline shift so the edit line continues from the left side again?

TIA

If I understand you correctly holding down the space bar will
do. The space bar toggles between playing and pausing. If you
hold it down when you toggle it to play then it will scroll along
(on my machine this is slowing playback down though). That is
the only way I know off.

I tested this under Premiere 6.0

I normally click and hold on the timeline scroll bar right arrow. This will continually scroll the timeline allowing you to keep up with the edit line. It isn't automatic, but will accomplish what you want to do. Let us all know if you find a better method.