We consider a dynamic hybrid supply chain model involving a service factor where two manufacturers and a retailer provide consumers with two alternative products. In this model, one manufacturer sells its product using a dual-channel supply chain but the other through the direct channel. The two manufacturers and the retailer simultaneously determine the direct price and retail price, respectively. The Nash equilibrium point and its stable region are obtained, and the occurrence of bifurcation is studied by parsing and through a numerical simulation. The influence of the price adjustment parameters, coefficient of services, and other parameters are investigated on a nonlinear dynamic game model. Such dynamic behaviors as bifurcation, periodic cycles, strange attractors of the system, phase portrait and sensitive dependence on initial conditions are studied. The results yield important theoretical and practical values for the management of services in hybrid supply chains.