Apparatus for detecting hypoglycemia or impending hypoglycemia by analysis of an EEG comprises at least one EEG measuring electrode (10) for gathering an EEG signal and a computer (12) for receiving said EEG signals programmed to obtain a plurality of signal components each comprising a different band of frequencies, obtain a measure of the varying intensity of each said component, obtain a long time estimate of the mean of each intensity measure, obtain a long time estimate of the variability of each intensity measure, normalise each intensity measure e.g. by a subtracting from the intensity measure the long time estimate of the mean and dividing the result by the long time estimate of the variability so as to generate from each band a normalised feature, use machine analysis of the normalised features to obtain a varying cost function, classify values of the cost function according to the probability of the cost function being indicative of hypoglycemia, integrate the probabilities obtained during a selected time period, and determine that the EEG signals are indicative of hypoglycemia being present or being impending based on said integration.