A methodology to detect sleep apnea/hypopnea events in the respiratory signals of polysomnographic recordings is presented. It applies advanced signal processing tools, such as empirical mode decomposition (EMD), Hilbert- Huang transform (HHT), fuzzy logic, feature extraction, expert criteria and context analysis. EMD, HHT and fuzzy logic are used for preliminary detection of respiration signal zones with significant variations in the amplitude of the signal; feature extraction, expert criteria and context analysis are used to characterize and validate the respiratory events. The system parameters were adjusted using the training set and fine-tuned applying the validation set; the testing data set was used to measure the final performance of the system. An annotated database of 30 all-night polysomnographic recordings, acquired from 30 healthy ten-year-old children at the Sleep Laboratory of the INTA-Universidad de Chile, was divided in a training set of 15 recordings (485 sleep apnea/hypopnea events), a validation set of five recordings (109 sleep apnea/hypopnea events), and a testing set of ten recordings (281 sleep apnea/hypopnea events). The overall detection performance on the testing data set of continuous all-night recordings was 89.7% sensitivity and 16.3% false-positive rate. The next step is to include discrimination among apneas, hypopneas and respiratory pauses.