Add submenu to existing menu - html

Question

Hi I have a basic menu for which I would like to add a submenu, that appears only when a certain menu link is hovered. Everything I have tried does not hide the submenu when a link is not hovered. Here is my code:
CSS
.navmenu{
float:right;
font-size: 13px;
font-weight:400;
text-transform: uppercase;
}
.navmenu li{
position: relative;
display: inline-block;
float: left;
}
.navmenu li a{
text-decoration:none;
color:#eee;
padding:15px 37px 19px 37px;
}
.navmenu li a:hover{
background:#36332e;
}
.active a{
background:#36332e;
}
HTML
<ul class="navmenu">
<li class="active">Home</li>
<li>About Us
<ul>
<li>Sub Link 1</li>
<li>SubLink 2</li>
</ul>
</li>
<li>Testimonials</li>
<li>Services</li>
<li>Contact Us</li>
</ul>

Answer 1

You need to initially hide the menu:
.navmenu li ul { display: none; }
and then display it when you hover over the nav item:
.navmenu li:hover ul { display: none; }
You should also be careful about defining styles that target .navmenu li or .navmenu li a because those will also target your submenu. You should instead use child selectors, giving you more control over the non-submenu links, so your selectors will look like:
.navmenu > li
.navmenu > li > a
I've encorperated some of those changes into this JSFiddle to get you started:
http://jsfiddle.net/Wexcode/B5P26/
Edit:
This is actually going to lose it's hover state when you hover over the submenu links:
.navmenu > li > a:hover {
background:#36332e;
}
Instead, you should do this:
.navmenu ul { position: absolute; }
.navmenu > li:hover { background: #e6332e; }
.navmenu > li > a { display: block; }
Since the <ul> is nested inside the <li> element, you won't lose the hover state when you hover over the submenu links. I updated the fiddle to reflect these changes.

Answer 2

<ul class="navmenu">
<li class="active">Home</li>
<li>About Us
<ul>
<li>
Sub Link 1
<ul>
</li> <a href=# >hi hi hi</a>
<ul>
<li>hello hello hello</li>
<li>hello hello hello</li>
<li>hello hello hello</li>
</ul>
</li>
</li><a href=# >hi hi hi</a> </li>
</li> <a href=# >hi hi hi</a> </li>
</ul>
</li>
<li>SubLink 2</li>
</ul>
</li>
<li>Testimonials</li>
<li>Services</li>
<li>Contact Us</li>
</ul>