The quasi-translatory properties of the Muskingum flood routing methods are demonstrated. The conditions for best approximation of the pure translation model by single and multiple Muskingum models are developed. Instead of the finite difference methods used in the literature the transfer function approach is analysed, which gives a new, general insight into the problem. The impact of physical interpretation of the Muskingum model parameters upon the quasi-translatory properties of the model is outlined.