Nationalists are surging and expected to make big gains when voters from 27 nations cast ballots starting this week for the European Parliament. But the prospect of success is already raising the question among far-right parties of how far is too far.

That question has become pressing as popular hard-right parties, especially in Italy and France, try to make themselves more palatable to the mainstream, splitting those who have sanitized and gained acceptability from those who are still considered taboo.

Today, the hard right is a movement marbled by fissures and shifting alliances.