Do you have that problem when running in the Firefox SafeMode?
http://support.mozilla.com/en-US/kb/Safe+Mode
Don't select anything right now, just use "Continue in SafeMode."

When in Safe Mode...

• The status of plug-ins is not affected.
• Custom preferences are not affected.
• All extensions are disabled.
• The default theme is used, without a persona.
• userChrome.css and userContent.css are ignored.
• The default toolbar layout is used.
• The JIT Javascript compiler is disabled.
• Hardware acceleration is disabled.

If not, see this:
https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fi...

Firefox doesn't do this by default.
This is likely changed by an extension (or theme), so you can check the settings in tab related extensions.

If it works in Safe Mode and in normal mode with all extensions (Tools > Add-ons > Extensions) disabled then try to find which extension is causing it by enabling one extension at a time until the problem reappears.

Close and restart Firefox after each change via "Firefox > Exit" (Windows: Firefox/File > Exit; Mac: "Firefox > Quit Firefox"; Linux: "Firefox/File > Quit")

• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Thank you both for your prompt replies. In safe mode, my tabs are back on top. So I'll start going thru the process of enabling one add on at a time.

This could take a while, as I am a sucker for add-ons.

Hi,

    I wanted to thank you both again, and report back on what happened.  I did as you said and opened FF in safe mode. The problem was an add on Tree Style Tab" (It was pretty silly of me to have it anyway, as it's no help if you use tabs at the top.) 

    Then I had a new problem, which was  that FF got incredibly slow, doing various irritating things, and not responding in spurts. However, armed with my new expertize in the use of safe mode, I troubleshot and found that the problem was the Copernic Desktop Explorer add on. I didn't mind disabling that one as I've felt that Copernic is over-rated since I installed it on my computer. 

   This whole process took me a long time, but it had definite benefits. I'm the sort of person who goes waltzing through the FF add-on site, grabbing this and that, because they look useful. Then I forget they are installed, don't figure out exactly what they can do, and don't look at the options. Unfortunately, I'm like a woman with a bunch of lovely clothes that were great buys hanging in the closet for months, with the price tags still on them. (The number of apps on my iPad may actually be more than the number of shoes in Imelda Marcos' closet.) 

    At any rate, in the process of solving my "misplaced tabs" problem, I reviewed my add-ons, adjusted options, and have improved my FF experience.

  It was really nice to get such to-the-point help so quickly through the forum. I very much appreciated being able to feel that the Mozilla community was there to support and help me. 

Best wishes to you both.

You can consider to create a second Firefox profile folder to test extensions first before deciding if you want to keep them.

• http://kb.mozillazine.org/Creating_a_new_Firefox_profile_on_Windows
• http://kb.mozillazine.org/Shortcut_to_a_specific_profile
• http://kb.mozillazine.org/Using_multiple_profiles_-_Firefox
• http://kb.mozillazine.org/Bypassing_the_Profile_Manager

Create a desktop shortcut with -P "profile" appended to the target to launch Firefox with each profile. Then you can set in the profile manager which profile to use by default if you click a link in an external program.

Use the -no-remote command line switch to open another Firefox instance with its own profile and to run different Firefox instances simultaneously, but do not use -no-remote with the default browser and the default profile.

• http://kb.mozillazine.org/Opening_a_new_instance_of_Firefox_with_another_profile

Thanks for the tip. I'll try it.