This paper presents a model of the respiratory tree as a recurrent, but asymmetric, structure. The intrinsic properties posed by such a system lead to a multi-fractal structure, i.e. a non-integer order model of the total impedance. The fractional order behavior of the asymmetric tree simulated as a dynamic system is assessed by means of Bode plots, on a wide range of frequencies. The results indicate than in a specific frequency range, both the symmetric and asymmetric representation of the respiratory tree lead to similar values in the impedance.