The early detection of subjects with probable Alzheimer's disease (AD) is crucial for effective appliance of treatment strategies. Here we explored the ability of a multitude of linear and non-linear classification algorithms to discriminate between the electroencephalograms (EEGs) of patients with varying degree of AD and their age-matched control subjects. Absolute and relative spectral power, distribution of spectral power, and measures of spatial synchronization were calculated from recordings of resting eyes-closed continuous EEGs of 45 healthy controls, 116 patients with mild AD and 81 patients with moderate AD, recruited in two different centers (Stockholm, New York). The applied classification algorithms were: principal component linear discriminant analysis (PC LDA), partial least squares LDA (PLS LDA), principal component logistic regression (PC LR), partial least squares logistic regression (PLS LR), bagging, random forest, support vector machines (SVM) and feed-forward neural network. Based on 10-fold cross-validation runs it could be demonstrated that even tough modern computer-intensive classification algorithms such as random forests, SVM and neural networks show a slight superiority, more classical classification algorithms performed nearly equally well. Using random forests classification a considerable sensitivity of up to 85% and a specificity of 78%, respectively for the test of even only mild AD patients has been reached, whereas for the comparison of moderate AD vs. controls, using SVM and neural networks, values of 89% and 88% for sensitivity and specificity were achieved. Such a remarkable performance proves the value of these classification algorithms for clinical diagnostics.