Citizenship, like membership, has its privileges. But “dual” citizenship also has its pitfalls for those who are traveling from country to country.
For instance, dual citizens who pull out two passports may be rebuked by a Customs and Border Protection Officer and told to get rid of one of their passports, even though the Department of State has affirmed that U.S. law does not require a person to choose between having citizenship with the United States and another country. This confusion exists in part because the Immigration and Nationality Act does make it unlawful for a U.S. citizen to use the passport of another country to enter or exit the U.S.
Similarly, foreign countries often require that their citizens use their domestic passports to enter and exit those countries.
It is, therefore, wise to use the passport of the country you are entering or exiting when traveling if you want to avoid a confrontation or delay caused by confusion with customs officers.
Generally speaking, you can probably keep your dual citizenship (if the laws of both countries permit it and there is no question of divided loyalty due to war). You can keep both of your passports as well, but in order to avoid trouble, you should be sure to use the passports of and follow the rules of the country in which you are traveling at all times.