Stress remains a significant social problem for individuals in modern societies. This paper presents a machine learning approach for the automatic detection of stress of people in a social situation by combining two sensor systems that capture physiological and social responses. We compare the performance using different classifiers including support vector machine, AdaBoost, and k-nearest neighbor. Our experimental results show that by combining the measurements from both sensor systems, we could accurately discriminate between stressful and neutral situations during a controlled Trier social stress test (TSST). Moreover, this paper assesses the discriminative ability of each sensor modality individually and considers their suitability for real-time stress detection. Finally, we present an study of the most discriminative features for stress detection.