If allowed by law in the relevant countries, it is possible to hold citizenship for two or more countries. In some countries, becoming a citizen of that country means the person will lose their existing citizenship.
Other countries prevent citizens giving up their nationality under any circumstances so the laws in each country need to be looked at closely.
When applying for dual citizenship it is important to note also that dual citizens may still be bound by the laws of their country and, for example report for military duty in countries where military service is mandatory.
Permanent residents can gain Australian dual citizenship by applying to become an Australian citizen and opting to retain their existing citizenship. Australian nationals are then allowed to apply for an Australian passport which is considered one of the most accepted passports in the world in terms of entering other countries.
Australian citizens can seek consular assistance from the Australian Government when travelling outside of Australia, however such assistance may be limited for dual nationals depending on the laws of the country they are in because some countries do not recognise dual nationality.
The Australian Department of Foreign Affairs and Trade may also be prevented from intervening in foreign jurisdictions to assist dual citizens if they enter the country using a passport other than their Australian passport.
Other advantages include the ability to register children born overseas as citizens by descent, and to be granted entry to Australia after being away from the country for any length of time. People who hold a dual citizenship are advised to use their Australian passport when entering and departing Australia.
The process of applying for dual citizenship in Australia is similar to the process for becoming an Australian Citizen. Permanent residents wishing to apply for Australian dual citizenship must meet the residency requirements including having been a permanent resident for four years and not being away from Australia for more than 90 days in the year before applying.
Migrants applying for dual citizenship must also intend to live in or maintain a close and continuing association with Australia, and be of good character. This generally means not having been involved in any illegal activity during the period of permanent residency.
As of 2015 Australian laws allow for dual nationals to be stripped of their Australian citizenship if they are suspected to be engaging in terrorism-related activity.
There are fees involved when applying for dual citizenship, however concessions and fee exemptions may be applicable. Special rules regarding Australian dual citizenship apply for New Zealand citizens.
More information on dual citizenship can be obtained from the Department of Immigration and Border Protection.