Alarm sounds triggered by biomedical equipment play a key role in providing healthcare in a neonatal intensive care unit (NICU). This paper presents our work on automatic detection of acoustic alarms in a noisy NICU environment, where knowledge about the particular characteristics of each alarm class is integrated at different stages of the detection system. The feature extraction is based on applying, around alarm-specific frequencies, a method for detection of sinusoidal signals, which employs the normalised short-term magnitude and phase spectrum. Also, the ratios of magnitudes at those frequencies are taken as features. The system consists of a set of GMM-based detectors, each designed to deal with a specific alarm. Temporal structure of alarms, in terms of duration of signal and silence intervals in every alarm period, is incorporated by aggregating the frame-level posterior probabilities. The experimental evaluations are performed with a database recorded in a real-world hospital environment. The performance of the detection system is assessed both at the frame level and at the alarm period level.