Offset breaks pagination

I have this code on my index.php :

<?php
get_header(); ?>

<div class="container">
<!-- Site-content -->
<div class="site-content clearfix">

<!-- main-column -->
<section class="main-column">

<div class="ribbon-container-newest-post">
<article class="newest-post">
<!-- Her I use a plugin to show the newest post -->
<?php dynamic_sidebar('newest-post-banner'); ?>
<?php echo get_the_excerpt(); ?>
</article>
<span class="ribbon"><?php the_category(); ?> </span>
</div>

<!-- Pagination -->
<div class="pagination">
<div class="nav-next alignleft"><?php previous_posts_link( '« Nyere posts' ); ?></div>
<div class="nav-previous alignright"><?php next_posts_link( 'Ældre indlæg »' ); ?></div>
</div>

<div class="posts_wrapper clearfix">

<?php

/* This is to show both "post" and "video" post types */
$args = array(
'post_type' => array ('post','video'),
'offset' => 1); // Start from the second
query_posts($args);
if ( have_posts() ) : while ( have_posts() ) : the_post();

?>

…

I’m completely new to wordpress, so I still don’t know the “right terms” to use!! My question is:
How can I show all posts types starting from the second post??

Without “offset=1” it was possible to show all the post types ( I have only 2 post types) and the “pagination” was working. But after I added “offset=1″, I get the same posts on all pages.
On the browser I see: “http://localhost:8888/wordpress/page/2/”, but the “page 2” shows the same as in the page 1.

Her is a picture of the blog:
http://grafisk.kts.dk/elever/flar1/wordpress/foto1.png

thanks!