  In this paper, a general construction of a skew product dynamical system, for
which the skew product dynamical system studied by Hahn is a special case, is
given. Then the ergodic and topological properties (of a special type) of our
newly defined systems (called Milnes type systems) are investigated. It is
shown that the Milnes type systems are actually natural extensions of dynamical
systems corresponding to some special distal functions. Finally, the
topological centre of the Ellis group of any skew product dynamical system is
calculated.
