French bulldogs, with their marble-like eyes and pleated faces, are beloved. Really, really beloved.

In the U.S., Frenchies didn’t even rank in the American Kennel Club’s top 30 most popular breeds in 2007. Last year, they were No. 4. In Britain they ranked 76th in 2005. Now they’re in second place.

But French bulldogs, as dogs go, are also quite unhealthy. They’re one of the brachycephalic breeds — dogs whose human-selected large heads and flat faces make them prone to certain ailments. “These dogs are kind of a dream for people who want to do research on pathology, on disease, in dogs,” said Dan O’Neill, a senior lecturer at the Royal Veterinary College in London. “They’ve got lots of problems.”

That’s bad for Frenchies, of course, but O’Neill said it has also become a crisis for what he calls “dogdom” — because it will mean more ailing animals at veterinary clinics, costlier bills for owners and more castoffs in shelters, not to mention a major incentive for unscrupulous breeders.

“These dogs came out of nowhere in 10 years,” said O’Neill, the lead author of a new study. “They are unhealthy, but it’s their rising popularity that makes it a huge issue.”

O’Neill and other researchers pulled records on all dogs treated at more than 300 clinics in 2013. They ended up with 2,228 French bulldogs and some revealing data points. Of the puppies born that year and seen in those clinics, 1.46 percent were Frenchies — up from 0.02 percent in 2003, which the authors call an “unprecedented” growth for a single breed. What’s more, the French bulldogs’ median age was 1.3 years, compared to about 4.5 for all dogs.

Despite their youth, 72 percent had some sort of disorder. Some of the most prevalent were common canine issues such as diarrhea or ear infections. But several were “conformational” disorders, or maladies related to the physical appearance that fanciers have decided French bulldogs should have.

The ailments included skin fold dermatitis, a stinky and uncomfortable bacterial infection that develops between the dogs’ wrinkles, and corneal ulcers, a painful condition that can result from eyes so bulging that they don’t fully close. Not surprisingly, five of the 25 most prevalent problems were upper respiratory disorders.

“That would not be the case with dogs overall,” O’Neill said. And the Frenchies’ youthfulness gave “a very rosy-eyed view” of their breed’s health, he added. “When these dogs reach middle age, these values are going to rise dramatically.”