This paper deals with necessary optimality conditions for control of general linear retarded systems to small solutions. Here the final states at timeTare required to generate small solutions of the uncontrolled system vanishing afterT − h + α, where α ≥ 0 is fixed. This generalizes the fixed final state problem where α = 0, and for α = hincludes problems with fixed reduced final stateFxT, whereFis the structural operator of the delay system. Necessary optimality conditions in the form of a maximum principle are valid if a certain space called the ‘ small attainability sub-space ’ is closed in a Sobolev space. A sufficient criterion for this closedness property is indicated. Finally, an example is discussed where the maximum principle for the fixed final state problem is not valid, while the new problem with α = hcan be solved by an application of the obtained results.