For years, iPhone owners have been the most satisfied smartphone owners. Apple‘s “it just works” design philosophy and brilliant marketing consistently put the company at the top of satisfaction surveys. Now, however, it seems that Apple’s monopoly on smartphone satisfaction is cracking.

The American Customer Satisfaction Index (ACSI) today released the results of a new study on smartphone satisfaction. The study ranks the top-selling smartphones of the past year using a proprietary scoring system for customer satisfaction. Apple does not top the list.

Samsung‘s Galaxy S III and Galaxy Note II smartphones have toppled the iPhone. Both received a ACSI score of 84. That’s two points higher than the iPhone 5 and iPhone 4S, which got scores of 82. The iPhone 4 follows just behind with an 81. Samsung smartphone owners were not as satisfied with the Galaxy S II, which scored only a 78 to put it at 7th place in the list.

“Not only does Samsung edge ahead of all iPhones, Apple customers themselves don’t see much difference between the iPhone 4, 4S or 5,” said David VanAmburg, director of ACSI. “The latest earnings report from Apple was better than expected, but the name of the game for Apple has always been innovation. Samsung, on the other hand, shows a strong upward ACSI trend from the Galaxy S II to the Galaxy S III. If the S4 performs as well—or even better—in the eyes of customers, Samsung could threaten Apple’s dominance in overall customer satisfaction.”

Motorola’s Droid Razr Maxx HD took 6th place with a score of 80, and the company’s Droid Razr came in 8th with a 77. Rounding out the top ten is BlackBerry, with its Curve and Bold devices scoring a 67 and 64, respectively.