Background: Sleep disordered breathing (SDB) is a frequent disorder with serious adverse health consequences in people with Down syndrome (DS). This study aims to evaluate and classify sleep and physical activity (PA) characteristics in adults with DS. Methods: Forty participants with DS wore an accelerometer for seven consecutive days to measure physical activity and sleep–wake patterns. The corresponding data were also obtained by survey and polysomnography. The apnea-hypopnea index (AHI) is calculated from the number of apneas and hypopneas per hour of sleep according to international guidelines. Results: Polysomnography showed SDB based on AHI in 95% of adults: 50% had severe SDB, 22.5% presented moderate and 22.5% mild SDB, predominantly in males. They had poor sleep quality (80.1%) and low PA levels. Using statistical classification methods, we observed three clusters with two opposite profiles. Clusters 2 and 3 showed low PA indices (daily steps: 5719 and 5310, respectively) and severe SDB (AHI = 33.6 and 55.5 events/h), high age and high gonial angle. Cluster 1 showed high PA (mean count of daily steps: 6908) and mild to moderate SDB (AHI = 16.8 events/h), low age and low gonial angle. Conclusions: Our findings suggest that there are different profiles (age, gender, obesity, gonial angle) that are associated with SDB in adults with DS. These results suggest that this may represent important factors to consider when planning health promotion and prevention.