I found these articles.
http://community.office365.com/en-us/forums/148/t/206087.aspx
http://social.technet.microsoft.com/Forums/sharepoint/en-US/1c3e17ce-042f-4377-895b-6bf55853a080/send-alerts-to-external-email-id?forum=sharepointdevelopmentlegacy
Is it true that you cannot add e-mail to external users that dont have office 365 e-mail?
So, external users cannot get alerts, unless having office 365 emails.
What would you recommend, to solve this?
best regards,
Ólafur