Are you using the Views menu in the Bookmarks Manager (Library)?

• The Views menu in the Bookmarks Manager (Bookmarks > Show All Bookmarks) is for viewing the bookmarks in a different sorting order (hence the name Views) and doesn't sort bookmarks permanently.
  Clicking the column header does the same sorting for viewing purposes only.
• If you want to sort bookmarks then you need to right-click a folder and use "Sort By Name" to sort that folder.

You can't sort individual bookmarks, only folders can be sorted this way.

Thanks for replying cor-el but

1/ I need a fuller description of what you mean by folders because it sounds like Firefox can't sort my bookmarks like other browsers will.

2/ I have no right-click option within the Bookmarks Library, so instead I went to Change your view > Sort > Sort by name. Even so my bookmarks are only sorted within the Bookmarks Library window and only temporarily. Bookmarks under the Firefox menu don't change at all.

The name of that menu is Views and that means in this case that the sorting is only for viewing purposes in the Bookmarks Manager (Library).
This is the same that happens if you click a column header.

If you do not have a two or three button mouse then see:

• http://kb.mozillazine.org/ui.click_hold_context_menus

Oh dear what a dummy I am! THANK YOU VERY MUCH cor-el  : )))))))))

P. S. It also put my random Bookmarks into A-Z ; b

You're welcome