<?php
        $categoryId = 10 ;  // get current category id
        $category = Mage::getModel('catalog/category')->load($categoryId) ;
        $catList = explode(",", $category->getChildren();) ;
        foreach{$catList as $cat} 
        {
           $subcategory = Mage::getSingleton('catalog/category')->load($cat) ;
           echo $subcategory->getName() ; 
        }
    ?>

It will display the second level. If you want to display further levels, put this code in recursive.