Walmart shoppers are getting wealthier. But will they stick around?

Walmart reported Tuesday that it continues to gain market share in grocery—but where those new customers are coming from may be surprising: Nearly three-quarters of the share gain is from households making more than $100,000 a year, the retailer noted.

This isn’t an entirely new development; Walmart executives reported in August that the chain—long known as a value-priced destination for lower-income, rural consumers—was now seeing shoppers from higher tax brackets as grocery prices climb around the country.

Or as Walmart CFO John David Rainey told investors Tuesday: “We believe our strong price positioning is contributing to share gains as we attract value-seeking customers across the household income spectrum.”

Attracting higher-income shoppers is one thing. But converting them into loyal Walmart customers is a whole other mission, one the nation’s largest retailer said it is ready to conquer.

This demographic is lured by Walmart’s omnichannel convenience, CEO Doug McMillon said. Pickup and delivery options just might be the glue that gets them to stick with the retailer. But none of that works without appealing items on the shelves, McMillon said.

“Fresh food and apparel are other areas, home’s another one, where if we can stand tall during this period of time, we think they’ll keep coming back to us,” he said. “Because we do have quality, we do have value and we’ve created a lot more ways for them to save time and the store and with pickup and delivery. So, that’s what we’re out to do.”

It’s little wonder people are turning to Walmart for grocery bargains. Food prices were up nearly 11% in October compared to a year ago, and dollar stores and discount grocers, too, are reporting that business is booming.

Sales of Walmart’s private brands are surging, increasing penetration in food categories by about 130 basis points during the third quarter, the company said. Walmart said it has seen “incremental trade down” in categories such as proteins, baking goods, baby food and dog food as food prices rise, leading to growth in private brands. But there is also a hefty segment of shoppers who remain loyal to national brands, Walmart U.S. CEO and President John Furner told investors.

“Now there are other consumers that are trading to Walmart that are not trading in private brands,” Furner said. “They're branded customers and they're buying more premium items … We positioned ourselves in terms of merchandising in the portfolio and with the channels by which we serve customers in a very flexible way so that we can help customers in whatever economic situation they’re in and we’ll be ready for the rest of the year.”

Whether Walmart can hold onto its wealthier shoppers remains to be seen. But Wall Street on Tuesday seemed fond of the trend, sending the retailer’s stock price up about 6%.