  In this article we introduce a new method for the construction of unique
strong solutions of a larger class of stochastic delay equations driven by a
discontinuous drift vector field and a Wiener process. The results obtained in
this paper can be regarded as an infinite-dimensional generalization of those
of A. Y. Veretennikov [42] in the case of certain stochastic delay equations
with irregular drift coefficients. The approach proposed in this work rests on
Malliavin calculus and arguments of a "local time variational calculus", which
may also be used to study other types of stochastic equations as e.g.
functional It\^{o}-stochastic differential equations in connection with
path-dependent Kolmogorov equations [15].
