e-Mail not delivered - Domain Not Resolved

e-Mail not delivered - Domain Not Resolved

This morning (european time 10:35 AM), we sent an e-Mail to a couple of recipients.
We got an error mail "Undelivered Mail Returned to Sender" stating that the e-Mail "could not be delivered to one or more of its recipients. This is a permanenterror.". It stated " mail@domain.com Domain Not Resolved" (about 20 times, some of the adresses were at gmx and hotmail).. How can this problem be solved?