This paper presents the dynamic modeling of a domestic hybrid water heating system. The system is composed of a solar collector, a heat pump water heater, a wind turbine, a battery and a hot water storage tank. Both air-source and geothermal-heat pumps are investigated. Detailed mathematical dynamic models of the individual components are presented and validated. Simulations for typical days in summer and winter for Beirut and Cedars, two Lebanese locations with different meteorological and demographic conditions, are conducted using Matlab software. A renewable coverage factor (RCF) is defined, representing the renewable energy share with respect to the total delivered energy. Results reveal that the proposed hybrid system is capable of securing all hot water needs in all case studies and RCF is always above 63%. Furthermore, an energetic, economic optimal management model is developed for the proposed hybrid system. It is applied to the considered case studies, where results illustrate the optimum size of each of the system components as well as the optimum energy-flow distributions among them over two investigated time periods, five and ten years. It is noticed that the initial cost of the hybrid system is acceptable and important annual savings are obtained. (C) 2014 Elsevier B.V. All rights reserved.