The output-feedback H-infinity control problem is solved for continuous-time, linear, retarded and neutral type systems. A delay-dependent solution is obtained in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying Park's inequality for bounding cross terms. A state-feedback solution is derived for systems with polytopic parameter uncertainties. An output-feedback controller is then found by solving two LMIs, one of which is associated with a descriptor time-delay "innovation filter." The cases of instantaneous and delayed measurements are considered. Numerical examples are given which illustrate the effectiveness of the new theory.