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Recent years have witnessed a good deal of research focused on abstract control dynamical systems defined in infinite-dimensional linear spaces. The main purpose of the present paper is to study the concept of constrained approximate relative and approximate absolute controllability for linear stationary abstract retarded dynamical systems defined in infinite-dimensional Hilbert spaces. ; First, using the methods of functional analysis, the brief and compact theory of such dynamical systems is recalled and the general integral form of solution is presented. It is generally assumed that the admissible controls are non-negative square integrable functions. Using the methods taken from the spectral theory of linear unbounded operators, the necessary and sufficient conditions for constrained approximate relative controllability are formulated and proved. ; These conditions are a generalization for infinite-dimensional retarded dynamical systems of the results derived recently for finite-dimensional dynamical systems with delays. Moreover, some additional remarks and comments on the relationships between different concepts of controllability are given. Finally, as simple illustrative examples, the necessary and sufficient conditions for constrained approximate relative controllability with non-negative controls for retarded distributed parameter parabolic-type dynamical systems with one constant delay and with homogeneous Dirichlet boundary conditions are presented.