This work is concerned with the simulation of gas networks using a hybrid modeling approach where different pipes are described withmodels belonging to the isothermal model hierarchy. It makes special emphasis in the coupling of algebraic and transient models and their effects in both steady-state and transient regime. The transient behavior of simple networks is studied in both non-dissipative and dissipative regime with a perturbation analysis. Physical effects concerning transmission and reflection of perturbations are studied both numerical and analytically. The transient response of the algebraic model is studied and compared with the results of numerical experiments. Finally a perturbative approach for computing the attenuation coefficient for dissipative transport is proposed and the analytical results are compared with the numerical experiments.