A method is proposed for stabilization, using static state feedback, of systems subject to time-varying delays in both the states and their derivatives (i.e., neutral systems), in the presence of saturating actuators. Delay-dependent conditions are given to determine stabilizing state-feedback controllers with large domain of attraction, expressed as linear matrix inequalities, readily implementable using available numerical tools and with tuning parameters that make possible to select the most adequate solution. These conditions are derived by using a Lyapunov-Krasovskii functional on the vertices of the polytopic description of the actuator saturations. Numerical examples demonstrate the effectiveness of the proposed technique.