mail sent twice (exim4)

On my website I use phpMailer to send mails. On my old server it worked fine (standard debian installation with exim4). But on my new server (also standard installation with exim4) the mails I send with phpMailer are received twice...
First I thought it was a bug in phpMailer, but the mail is sent once to the SMTP port.

Sending mails with telnet and the command-line mail is no problem. Those mails are received once.

Here's some exim4 log to show the same mail from phpMailer is sent twice.

2007-12-21 23:54:12 1J5qku-0001WE-CS <= H=(xxx.yyy.xs4all.nl) [127.0.0.1] U=www-data P=smtp S=497
2007-12-21 23:54:12 1J5qku-0001WE-CS => R=smarthost T=remote_smtp_smarthost H=smtp.xs4all.nl [194.109.6.51]
2007-12-21 23:54:12 1J5qku-0001WE-CS Completed
2007-12-21 23:54:12 1J5qku-0001WM-OA <= H=(xxx.yyy.xs4all.nl) [127.0.0.1] U=www-data P=smtp S=497
2007-12-21 23:54:13 1J5qku-0001WM-OA => R=smarthost T=remote_smtp_smarthost H=smtp.xs4all.nl [194.109.6.51]
2007-12-21 23:54:13 1J5qku-0001WM-OA Completed


I even wrote my own SMTP-class in PHP, but mails sent through this class are also received twice. (I tested my class on another webserver and it works perfectly, so no flaws in my script)

I even checked my processes, but exim4 is only running once.
What's wrong here???