The main purpose of the paper is to study the constrained controllability for linear, time-invariant retarded dynamical systems defined in infinite-dimensional Banach or Hilbert spaces. First the brief theory of such dynamical systems is recalled. N ext, different definitions of controllability are presented and the relationships between them are explained. ; Using the general spectral theory of unbounded linear operators, many constrained controllability conditions are formulated and proved. Finally, a simple illustrative example is given. The results presented extend to the case of abstract retarded dynamical systems, constrained controllability conditions given in the literature for finite-dimensional case or systems without delays.