We consider two minimum loss scheduling problems. Let the arrival epochs and processing times of n consecutive jobs be known. The first problem deals with the case these jobs can be processed by m parallel nonidentical machines without waiting room, i.e., a pure loss system. In the second problem there is one machine with a finite waiting room, i.e., a single machine delay-loss system. For both problems we give an algorithm that minimizes the total number (c.q. weight) of lost jobs.