  In this article, a class of optimal control problems of differential
equations with delays are investigated for which the associated
Hamilton-Jacobi-Bellman (HJB) equations are nonlinear partial differential
equations with delays. This type of HJB equation has not been previously
studied and is difficult to solve because the state equations do not possess
smoothing properties. We introduce a slightly different notion of viscosity
solutions and identify the value function of the optimal control problems as a
unique viscosity solution to the associated HJB equations.
