Abstract : We study a class of optimal control problems with state constraint, where the state equation is a differential equation with delays in the control variable. This class of problems arises in some economic applications, in particular in optimal advertising problems. The optimal control problem is embedded in a suitable Hilbert space and the associated Hamilton- Jacobi-Bellman (HJB) equation is considered in this space. It is proved that the value function is continuous with respect to a weak norm and that it solves in the viscosity sense the associated HJB equation. The main result is the proof of a directional C1 regularity for the value function. This result represents the starting point to define a feedback map in classical sense going towards a verification theorem and the construction of optimal feedback controls for the problem.