Thank you very much!
I’ve correct a bit your code ($category is an object, $category->term_id is the category ID), and added default, that contains all parameters (i want to see categories with no posts so i’ve set to false hide_empty parameter).
this is my running code ??
$defaults=array('type'=>'post',
'child_of'=> 23,
'orderby'=>'name',
'order'=>'ASC',
'hide_empty'=> false,
'include_last_update_time'=>false,
'hierarchical'=>1,
#'exclude'=> ,
#'include'=> ,
#'number'=> ,
'pad_counts'=>false);
foreach(get_categories($defaults) as $category) : ?>
<div class="cat_box">
<h4><? echo $category->name ?></h4>
<?php $getposts =get_posts('numberposts=5&category='.$category->term_id);
foreach($getposts as $post) : setup_postdata($post); ?>
<? the_title() ?>
<?php endforeach; ?>
</div><!-- box -->
<?php endforeach; ?>