I first looked at the EasyExpat article on moving pets- Bringing Along Fido
- but Sweden appears to be a bit unusual.
However, I think I found the info you are looking for: http://www.sjv.se/swedishboardofagricul ... 03137.html
. Looks easy if you are coming from EU countries, Andorra, Faeroe Islands, Iceland, Liechtenstein, Norway and Switzerland and slightly more difficult from elsewhere.