SHANGHAI — Doughnut shops, once a rarity here, have proliferated across the city, with a huge number of rivals – including American giants Dunkin’ Donuts and Krispy Kreme – battling for supremacy in the race to give Shanghai’s middle-class consumers their morning coffee-and-sugar fix.

The opening of so many doughnut shops in so many locations is a testament to Shanghai’s growing affluence and the belief that young Chinese with more disposable income will be hankering for more leisure food. As China has opened its doors to the world, American fast-food chains such as KFC, McDonald’s and Starbucks have exploded here, mostly in wealthier cities and coastal areas, with varying degrees of success.

So an American-style doughnut, with a cup of coffee, would seem a perfect fit for China’s modern, on-the-go city lifestyle.

But others look at the swelling number of doughnut shops here wonder whether it’s just too much. Some shops have disappeared. Many others appear mostly empty at peak hours – and Chinese customers seem more interested in the drinks than the doughnuts. And following the lessons of other American retailers, the doughnut shops are finding that some of their best-sellers would be barely recognizable back home, like Dunkin’s dried pork and seaweed doughnut, or the doughnut made with dried bonito fish.

Some industry analysts think Shanghai’s doughnut market might already be saturated and speak of an ensuing “doughnut war,” which might leave just a few survivors.

And what isn’t at all clear is whether Chinese consumers particularly like doughnuts.

The average Chinese breakfast might consist of congee, or rice porridge, maybe some soy milk, sometimes fried noodles, or perhaps a dry roll or bun. The idea of something as sweet as a glazed or cream-filled doughnut in the morning would seem an anathema to many local palates.

“I’m not a big doughnut lover, and I only have one once a month,” said a 28-year-old woman working as a marketing manager, who stopped by Krispy Kreme on a recent Friday. “There are too many calories and they’re too sweet, unacceptably sweet, especially the chocolate ones. But the doughnut looks really cute!”