You can set the pref browser.tabs.animate to false on the about:config page.

To open the about:config page, type about:config in the location (address) bar and press the "Enter" key, just like you type the url of a website to open a website.
If you see a warning then you can confirm that you want to access that page.

• http://kb.mozillazine.org/about%3Aconfig

Thanks cor-el. I've already tried that setting. It only prevents animation of the tabs themselves, not animation ON the tabs.

to get an alternative to the animation google the following: disable throbber in firefox

my request to you: instead of thank you please remove one of your threads cause you have duplicate questions if you google the following: FF 4 - Is there any way to disable the connecting/loading animation on the tabs?

Add code to userChrome.css below the @namespace line.
See:

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

@namespace url("http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul"); /* only needed once */

.tab-throbber { display: none !important }

You can also use this extension:

• ChromEdit Plus: http://webdesigns.ms11.net/chromeditp.html

Thanks Cor-el! That did it.

Please developers include an option in about:config to turn the throbber off, at least the reversal of direction. Put cor-el's patch in the code.