  It is known that hyperbolic non\-autonomous linear delay differential
equations in a finite dimensional space are Hyers--Ulam stable and hence
shadowable. The converse result is available only in the special case of
autonomous and periodic linear delay differential equations with a simple
spectrum. In this paper, we prove the converse and hence the equivalence of all
three notions in the title for a general class of nonautonomous linear delay
differential equations with uniformly bounded coefficients. The importance of
the boundedness assumption is shown by an example.
