While the '_MPlane command has a Command line option called “Show” to switch the visibility of the axis icon of an existing MPlane, I can’t find a similar option for my existing CPlanes, hence the axis icon remains visible even if I revert to another CPlane. Is there a way to fix that?
I just figured out that the axis icon disappears after clicking on the blank area at the very bottom of the “Named CPlanes” list. This should be documented in the Help files. 
This solution worked for all of the CPlanes except for the first one which I cannot make disappear. I am using version 8.
Hi Timothy- if a cplane is highlighted in the panel, its axes will show in the viewport.
-Pascal
Thanks for that. What was happening was that one axis remained on the model no matter what I did on the panel. The way I made it disappear was to close down the drawing and reopen it and it was gone,