Before revision:  We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs with generators of a moving average type .
After revision:  We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs and we investigate in detail some properties of the solutions. In particular, these solutions are linear, time-consistent, continuous, non-monotonic and not conditionally invariant with respect to a terminal condition. A motivation for dealing with generators of a moving average type .