In this work, an analytical solution for the low frequency polymer electrolyte membrane (PEM) fuel cell impedance is derived. A relationship between the low frequency phase shift induced by the oscillations of gas concentration in the channels is found, and it is shown that the phase is a function of the oxygen stoichiometry, lambda, and the oxygen residence time, tau(c)., in the channels. Experimental measurements of PEM fuel cell impedances are performed, and the analytical model is found to be in great agreement ford lambda <= 3 and tau(c) > 0.2 s for a large set of experimental conditions and channel geometries. Finally, we report reduced models for the maximum phase shift induced by the gas oscillations in the channels and for the characteristic frequency at which this phenomenon is the most pronounced. This work gives new insights regarding the mechanisms that govern the low frequency fuel cell impedance at lambda <= 3, and thus paves the way for improved fuel cell mass transport characterisations.