In this chapter, we introduce a family of models dened by compounding two (a continuous and other discrete) distributions. The new family has as limiting case the adopted baseline distribution. The generated models are frequently more exible than the baseline distributions. Several mathematical properties such as moments, quantile and generating functions, among others, are provided. Further, the estimation procedure is approched by maximum likelihood. The potentiality of the family of models is illustrated by means of two applications to real data.