Some initial results on the disturbance properties of high order iterative learning control (ILC) algorithms are presented. Of particular interest is to investigate how high order ILC algorithms cope with measurement and load disturbances of different character. Some results are obtained by assuming statistical properties of the involved disturbances and deriving equations for the covariance matrix of the control error vector. The results are illustrated by analytic derivation of the covariance matrix for a second order ILC algorithm with a particular choice of design variables.