The anser to your question can depend on the countries involved. For example, a US State Department website says this about dual citizenship Israeli-Americans:
"Israeli citizens naturalized in the United States retain their Israeli citizenship, and children born in the United States to Israeli parents usually acquire both U.S. and Israeli nationality at birth. Israeli citizens, including dual nationals, must enter and depart Israel on their Israeli passports."
Source: http://travel.state.gov/content/passports/english/country/israel.html

The anser to your question can depend on the countries involved. For example, a US State Department website says this about dual citizenship Israeli-Americans:
"Israeli citizens naturalized in the United States retain their Israeli citizenship, and children born in the United States to Israeli parents usually acquire both U.S. and Israeli nationality at birth. Israeli citizens, including dual nationals, must enter and depart Israel on their Israeli passports."

Source: travel.state.gov