We consider a finite set of unit time execution tasks with release dates, due dates and precedence delays. The machines are partitionned into k classes. Each task requires one machine from a fixed class to be executed. The problem is the existence of a feasible schedule. This general problem is known to be N P-complete; many studies were devoted to the determination of polynomial time algorithms for some special subcasses, most of them based on a particular list schedule. The Garey-Johnson and Leung-Palem-Pnueli algorithms (respectively GJ and LPP in short) are both improving the due dates to build a priority list. They are modifiying them using necessary conditions until a fix point is reached. The present paper shows that these two algorithms are different implementations of a same generic one. The main consequence is that all the results valid for GJ algorithm, are also for LPP and vice versa.