In this paper we describe the mathematical modelling components of the Open University second level course in applied mathematics called Mathematical Models and Methods. The teaching of mathematical modelling has been introduced in many British Universities and Poly technics. But teaching modelling at a distance is fraught with difficulties. What these are and how we overcame them is described by the authors. In doing so we,hope that other distance education institutes will find it attractive to offer components on mathematical modelling in some of their courses.