We show that the peculiar surface abundance patterns of Carbon Enhanced Metal Poor (CEMP) stars has been inherited from material having been processed by H- and He-burning phases in a previous generation of stars (hereafter called the “Source Stars”). In this previous generation, some mixing must have occurred between the He- and the H-burning regions in order to explain the high observed abundances of nitrogen. In addition, it is necessary to postulate that a very small fraction of the carbon-oxygen core has been expelled (either by winds or by the supernova explosion). Therefore only the outermost layers should have been released by the Source Stars. Some of the CEMP stars may be He-rich if the matter from the Source Star is not too much diluted with the InterStellar Medium (ISM). Those stars formed from nearly pure ejecta would also be Li-poor.