EU/EEA and Swiss citizens
You do not need a work permit or visa. As an EU citizen you have the right to work, study or live in Sweden also without a residence permit.The right of EU citizens to stay in Sweden without a residence permit is called right of residence. You have right of residence if you are employed, self-employed, a student or have sufficient means to support yourself.
You do not need a permit to work for less than three months
The following people may work in Sweden without a permit: visiting research fellows or teachers at higher education institutions who participate in research, teaching or lecturing activities for up to three months altogether over the period of 12 months. However, citizens of certain countries need a visa. See information about visa
If you plan to work in Sweden for longer than three months, you will need a permit
The main rule is that you should apply for and have been granted a permit before entering Sweden. When applying online you are given clear instructions about how to fill in your application and what you should send with the application. This makes it easier for you to apply correctly and increases your chances of a quick decision
More information about permits, visas and application forms can be found at http://www.migrationsverket.se/English/Private-individuals.html.
Extending your permit
Note, special rules apply for visiting researchers.
If you plan to continue working as a visiting researcher after your residence permit expires, apply to extend it. Make sure to submit your application before your current permit expires. You can obtain a permit for the period during which the agreement with the research principal is in force but not past the time for which your passport remains valid. Once you have had a residence permit to conduct research for four years, you can obtain a permanent residence permit, which remains in force as long as you live in Sweden.
Keep in mind that your ability to obtain a permanent residence permit may be affected if you did not live or work in Sweden during extended periods of time while your permit was in force.
How to apply
You can apply to extend your permit online. Apply before your current permit expires. If you have family members living with you in Sweden who also need to extend their permits, you apply for them in the same online application.
Extending a work permit (for those not in the category "visiting researcher")
When you apply for an extension of your work permit, the Migration Agency checks that the conditions for a work permit have been met during the periods of validity of each of your previous work permit periods. For applications to be complete, you need to submit documents that show that salary and insurance requirements have been met for each month you have held a work permit in Sweden. Contact your employer regarding this and before you start your application for an extension. Read more at www.migrationsverket.se