Based on the influence function (Hampel et al. 1986), we analyze several forms of learning rules under the influence of abnormal inputs (outliers). Principal component analysis (PCA) learning rules (Oja 1982, 1989, 1992) are shown to be sensitive to the influence of outliers. Biologically motivated robust PCA learning rules are proposed. The variants of BCM learning (Bienenstock et al. 1982; Intrator 1990b) with linear neurons are shown to be subject to the influence of outliers, in contrast they are shown to be robust to outliers with sigmoidal neurons.