New lawsuits say the advertising is deceptive, as the fight over "natural" food claims shifts upstream.

Stroll down your supermarket's aisles, and you may notice some new words on the cereal and snack boxes. "Natural," once the descriptor of choice, is being crowded out after years of lawsuits. In its place: "Honest." "Simple."

The "natural" claims haven't vanished, just become less conspicuous—and as the claims have evolved, so has the litigation over whether they're deceptive. New lawsuits filed Wednesday target what they say are small amounts of the world's most popular pesticide in granola bars ostensibly "made with 100% natural whole grain oats."

In 2014, General Mills settled a class-action lawsuit and agreed not to label its Nature Valley granola bars "100% natural" if they contained high-fructose corn syrup, maltodextrin or several other highly-processed ingredients. The phrase soon disappeared from its spot on the box right under the brand name. And yet it has reappeared—in a different place, outside the scope of that settlement—on many Nature Valley products. The Sweet & Salty Nut granola bars, for example, come with text that says they are "made with 100% natural whole grain oats."

According to lawsuits filed Wednesday in New York, California, Minnesota and Washington, D.C., that claim is deceptive.

"The oat products at issue are not 'made with 100% natural whole grain oats,'" the D.C. complaint alleges. The products contain, it says, small amounts of the common pesticide glyphosate. At 0.45 parts per million, the level it says they contain is well below the Environmental Protection Agency's 30 ppm limit. But the suit contends that's still higher than should be allowed because the pesticide likely comes from the "100% natural" oats.