Från ESTA Online Hjälp :
What if I have dual citizenship, but my non-VWP passport is expired or I do not have a passport for that country?
If you have any additional passports, please enter the most recent passport information, even if that passport is expired. If you are a dual citizen but do not have a passport from another country, select the country from the drop down list and do not enter anything in the Passport Number field.