Styling with CSS

I have 2 div classes for links in my webpage. The first is for my general nav links which will go across the top of my page and the 2nd is for my quicklinks which run down the left hand side of the page. Then I have various links within the text of each paragraph on the page. The HTML looks like this

<div class="nav">

<a href="various_pages.html">text</a>

 </div>

<div class="quicklinks">

<a href="various_pages.html">text</a>

</div>

I want to style my "nav" class with no underline neither on hover, activate, focus nor on visited. For my "quicklinks" class I want the underline on hover, activate and focus. In neither case do I want any colour change. I then want the remaining links in the document to be styled in the same way as my "quicklinks".

My CSS looks like this: -

a:link {color: #364467; text-decoration: none}
a:visited {color: #364467; text-decoration: none}
a:hover {text-decoration: underline}
a:active {text-decoration: underline}
a:focus {text-decoration: underline}

a.nav:link {color: #364467; text-decoration: none}
a.nav:visited {color: #364467; text-decoration: none}
a.nav:hover {text-decoration: none}
a.nav:active {text-decoration: none}
a.nav:focus {text-decoration: none}

BUT, my "nav" links just look like everything else i.e. they still have the underline on hover, active and focus.

Can't figure this out.

Help!