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$('.target').next()
    .css('background-color', 'yellow')
    .append(' <span class="label label-info">next after .target</span>');


$('li').next('.target')
    .css('background-color', 'yellow')
    .append(' <span class="label">next with .target class</span>');

<ul>
<li>list item
<ul>
<li>list item</li>
<li class="target">list item with target class</li>
<li>list item</li>
<li>list item</li>
</ul>
</li>
<li>list item</li>
<li class="target">list item with target class</li>
<li>list item</li>
<li>list item</li>
</ul>