The paper deals with the nonlinear mathematical modelling of the longitudinal dynamics of a small sized hybrid airship with suspended payload vehicle. The modelling is done by considering the system as single body dynamic as well as two body dynamics. Bifurcation Analysis method is applied to do the trim and stability analysis of the system. MATLAB and AUTO bifurcation analysis tool is used for dynamic modeling and simulation of the system. Total five different simulation cases with different elevator deflection are discussed for 3DOF model. For each case Six output states as Vel, gamma, alpha, q, theta and range (h) is taken and one input parameter as dele i.e. elevator deflection is taken. In this paper 6DOF and 3DOF longitudinal conventional single body dynamic model of hybrid airship is discussed and an alternate method as 4DOF two body longitudinal dynamic model of hybrid airship is also considered. Simulation is done for all models on MATLAB and Alternate technique as bifurcation method is also used on AUTO software to study the dynamic analysis of the system. Eigen values is obtained from bifurcation method and is helpful to analyze the stability of the Hybrid airship with suspended payload vehicle.