Early life stress in the neonatal intensive care unit (NICU) predisposes premature infants to adverse health outcomes. Although those patients experience frequent apneas and sleep-wake disturbances during their hospital stay, clinicians still rely on clinical scales to assess pain and stress burden. This study addresses the relationship between stress and apneic spells in NICU patients to implement an automatic stress detector. EEG, ECG and SpO2 were recorded from 40 patients for at least 3 hours and the stress burden was assessed using the Leuven Pain Scale. Different logistic regression models were designed to detect the presence or the absence of stress based on the signals reactivity to each apneic spell. The classification shows that stress can be detected with an area under the curve of 0.94 and a misclassification error of 19.23%. These results were obtained via SpO2 dips and EEG regularity. These findings suggest that stress deepens the physiological reaction to apneas, which could ultimately impact the neurological and behavioral development.