This paper presents the modelling and parameter identification of the gas exchange dynamics during cycling. A discrete-time linear parameter-varying model is proposed, which relates the dynamics of oxygen consumption and carbon dioxide production with the developed pedal power. A state-dependent nonlinear function is used for modelling the excess carbon dioxide production. The approach proposed for parameter identification is based on specific exercise scenarios tailored to the considered individual, which reduces the data acquisition process. The parameter identification process is performed as a solution of a sequence of nonlinear unconstrained optimisation problems using measured data from different cycling scenarios. An illustration of the methodology used for the identification and the validation of the model is also presented.