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Obtaining a Swedish work permit is no easy matter. Swedes, foreign citizens already living in Sweden and EU/EEA citizens have preference over others in obtaining work in Sweden.
If the offer of work is for more than three months you will also require a Swedish residence permit.
If you will be in Sweden for less than three months, you will not require a residence permit. You may, however, require an entry visa. Information about which citizens are required to have entry visas and more information on visas is found on the page 'Visa for visiting Sweden'.
Requirements for a work permit
Where do I apply?
The first time you apply for a work permit, you do so at the Swedish Embassy or Consulate in your country of origin or in your country of domicile.