Create a Query Loop for only 1 or 2 categories.

http://codex.wordpress.org/Class_Reference/WP_Query
http://codex.wordpress.org/Class_Reference/WP_Query#Category_Parameters

for one category, you can use the category slug
as in this line: 'category_name' => 'category-1'

for 2 or more categories, use the category ids and this instead: 'category__in' => array(23, 56, 77)

example:

<?php $args = array(
'posts_per_page' => -1,
'category_name' => 'category-1'
);
$cat_query = new WP_Query( $args );
if( $cat_query->have_posts() ) : while( $cat_query->have_posts() ) : $cat_query->the_post(); ?>
YOUR OUTPUT
<?php endwhile; endif; wp_reset_postdata(); ?>