Divided attention has little effect for simple tasks, such as luminance detection, but it has large effects for complex tasks, such as semantic categorization of masked words. Here, we asked whether the semantic categorization of visual objects shows divided attention effects as large as those observed for words, or as small as those observed for simple feature judgments. Using a dual-task paradigm with nameable object stimuli, performance was compared with the predictions of serial and parallel models. At the extreme, parallel processes with unlimited capacity predict no effect of divided attention; alternatively, an all-or-none serial process makes two predictions: a large divided attention effect (lower accuracy for dual-task trials, compared to single-task trials) and a negative response correlation in dual-task trials (a given response is more likely to be incorrect when the response about the other stimulus is correct). These predictions were tested in two experiments examining object judgments. In both experiments, there was a large divided attention effect and a small negative correlation in responses. The magnitude of these effects was larger than for simple features, but smaller than for words. These effects were consistent with serial models, and rule out some but not all parallel models. More broadly, the results help establish one of the first examples of likely serial processing in perception.