The author discusses linear multistep methods for functional differential equations which are correct for the jumps in the derivatives of the solution. The asymptotic behavior of the global discretization error is discussed as well as the implementation of these methods in predictor- corrector mode with step changing strategy based on the estimation of the local error by Milne’s device. The author proves that Milne’s device does detect the jumps in the derivatives of the solution but one step later than it should and recommends step changing strategy which accounts for this phenomenon.