Check out the solution here: http://jsfiddle.net/bpJUv/1/
JavaScript Code:
$('#tabs').tabs();
$('#tabs1').tabs();
$('#tabs2').tabs();
HTML Markup:
<div id="tabs">
<ul>
<li><a href="#tabs-1">First tab</a></li>
<li><a href="#tabs-2">Second tab</a></li>
</ul>
<div id="tabs-1">
<p>
<div id="tabs1">
<ul>
<li><a href="#tabs-11">First nested 1</a></li>
<li><a href="#tabs-12">Second nested 1</a></li>
</ul>
<div id="tabs-11">
<p>Content for first nested tab 1</p>
</div>
<div id="tabs-12">
<p>Content for second nested tab 2</p>
</div>
</div>
</p>
</div>
<div id="tabs-2">
<p>
<div id="tabs2">
<ul>
<li><a href="#tabs-21">First nested tab 2</a></li>
<li><a href="#tabs-22">Second nested tab 2</a></li>
</ul>
<div id="tabs-21">
<p>Content of first nested tab 2</p>
</div>
<div id="tabs-22">
<p>Content of second nested tab 2</p>
</div>
</div>
</p>
</div>
</div>