We introduce nonautonomous well-posed and (absolutely) regular linear systems as quadruples consisting of an evolution family and output, input, and input output maps subject to natural hypotheses. In the spirit of Weiss' work, these maps are represented in terms of admissible observation and control operators (the latter in an approximate sense) in the time domain. In this setting, the closed-loop system exists for a canonical class of "admissible" feedbacks, and it inherits the absolute regularity and other properties of the given system. In particular, we can iterate feedbacks.