Robust estimation of power spectra, coherences, and transfer functions is investigated in the context of geophysical data processing. The methods described are frequency-domain extensions of current techniques from the statistical literature and are applicable in cases where section-averaging methods would be used with data that are contaminated by local nonstationarity or isolated outliers. The paper begins with a review of robust estimation theory, emphasizing statistical principles and the maximum likelihood or M-estimators. These are combined with section-averaging spectral techniques to obtain robust estimates of power spectra, coherences, and transfer functions in an automatic, data-adaptive fashion. Because robust methods implicitly identify abnormal data, methods for monitoring the statistical behavior of the estimation process using quantile-quantile plots are also discussed. The results are illustrated using a variety of examples from electromagnetic geophysics. ¿ American Geophysical Union 1986