What kind of animation do you want? FadeIn of the background image? That's not how to do that. Try instead setting the :hover background image for an element inside your a.nav_menu, with a.nav_menu having the default state. Then on hover, fade in the inside element.
say your markup becomes:
a href="" class="nav_menu" title="HOME"><strong>HOME</strong></a>
You can now style your A and STRONG tags. A receives the default background-image. In your css:
a.nav_menu{
background-image: url(nav_.jpg);
}
a.nav_menu strong{
background:none;
display:block;
}
In your javascript:
$(function(){
$("a.nav_menu")
.mouseover(function(){
$(this).find('strong:first').stop().animate({'background-image':'url(nav_hover.jpg)', opacity: 1},3000);
})
.mouseout(function(){
$(this).find('strong:first').stop().animate({'background-image':'none', opacity: 0},3000);
})
});
I didn't test it, and you should check if jquery's animate() function can do what you intend, using background-image like that.
Also, see this article, which uses background-position and a sprite image instead. It seems more proper to achieve the effect you intend.