In this paper the MINLP method proposed in Part (I) is illustrated by applying it to; the synthesis problem of non-sharp distillation sequences. A MINLP formulation for the synthesis of distillation sequences with non-sharp separation is proposed. In this Formulation the recoveries of the key components are introduced as optimization variables and this makes it possible to synthesize a distillation sequence with specified component recoveries, and at the same time, renders the MINLP problem nonconvex. The solution procedure is illustrated with three example problems.