From 1 January 2020, it is allowed to have one or more citizenships in addition to Norwegian citizenship. This rule applies to both Norwegian citizens who obtain another citizenship, and to those who are applying for Norwegian citizenship.
In order for you to have dual citizenship, the other country you are a citizen of must also allow this. You must always check with the authorities in the country you are or wish to become a citizen of if they allow dual citizenship.
Norwegian citizens who become a citizen of another country, must give written notice to the Norwegian authorities. For more information, see the Tax Administration's website.
Please note that the changes to the Citizenship Act implemented from 1 January 2020 are not retroactive. If you obtained another citizenship by application before 1 January 2020, your Norwegian citizenship was lost from the date your new citizenship was granted. In such case, it may be possible to get back your Norwegian citizenship.
For more information regarding dual citizenship, please see UDI's website.