For the first time, one of several lawsuits filed in recent years accusing McDonald’s of unfair pay practices has been granted federal class-action status, which is often the only practical and affordable way to sue when many people are affected.

The development is another step forward in the battle for fair pay for low-wage workers that began in 2012 with a walkout by fast-food employees in New York City and mushroomed into a national movement.

The lawsuit, begun in 2014, charges that employees were systematically and deliberately underpaid at five McDonald’s restaurants, owned by a single franchisee, in Northern California. The alleged violations included unpaid overtime, misrecording of timecards to reduce pay, failure to pay the minimum wage and failure to pay wages owed to employees who quit or were fired. In documenting the alleged violations, the lawsuit goes back to 2010 and asserts that most of the practices continue today.