Whether or not you need a work permit/work visa for your tour obviously depends on where your tour is and what citizenship you hold. For instance, EU citizens can play outside of their home country across the EU without problems, some Commonwealth Country passport holders can play in the UK without applying for a work visa, and so on. Other factors involved in determining whether or not you need a work permit include how many shows you are playing, how much money you will be paid for your tour, and how long your tour lasts. In some cases, the group putting together your tour may require you to have a permit to play. For instance, if you travel to America for SXSW or you travel to a country to play a music festival, the organizers will almost always require you to have a permit.
Your first port of call in determining if you need a work permit or not should be the embassy website for the country you plan to visit. The website should have information that applies dircetly to citizens of your country. Keep in mind that entertainment and music related work permits/work visas are almost always handled in a different way than other work permits, so be sure to check out the information about these specific kind of visas.
Other things you should remember about work permits - some countries have application fees as well as fees for issuing the permit, so they can represent an extra expense. Also, some countries can take a very long time to approve these application or may charge a priority processing fee to get your visa sooner (the USA being a major example of a country that has extremely high priority processing fees). If you know you will be touring overseas, figuring out your work permit situation should be at the top of your list of things to do. Otherwise, you may find yourself forced to cancel shows when your paperwork doesn't come in on time.
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