Electrical Activity of a human brain measured on the skull(electroencephalogram, EEG) contains in the sleep period manytransients (sleep spindles, spike-like structures or vertex waves), i.e. bursts of EEG activity of limited duration, having random occurrenceand may be coupled with specific sleep stages. A computer-baseddetector was designed that detects a transient called K-complex. Thedetector is based on linear matched filtering and its nonlinearmodifications. The linear and nonlinear approaches are compared andevaluated with respect to the detection efficiency.