Chains of operations have to be scheduled on a single machine such that a minimum delay is set between any two operations linked by a precedence relation. Three sub-problems are shown to be solved in polynomial time. First, we consider the problem of minimizing the makespan when all the operations have the same duration p and all the delays are equal to a constant l. Next, we consider that the length of any delay is less than the shortest processing time and we present an algorithm to minimize the makespan and another one to minimize the flow time when all the processing times are equal.