What happens if a royal or noble marries a commoner of another nationality?

It is dependent upon the country in which the marriage takes place. In most countries today, there are no laws against marriage between a royal and commoner. For example, if a prince married a commoner girl, she would still be a princess and their children princes and princesses. In most European countries, a princess does not pass her princely status on, no matter who she marries, but if she marries a commoner, he will usually be made a duke, count, etc. and their children will be lords or ladies and be in line for the throne. In royal countries which are less modern, men can still marry commoners but princesses must marry within the royal family or their children will have nothing. For example, Princess Sayako of Japan lost her title, allowance and all other royal vestiges because she married a commoner and the law says that will happen if she marries outside of the family, which princesses always do. Basically, as far as Europe is concerned, there is no issue