The steady state and dynamic behaviour of an adiabatic packed bed reactor for the selective hydrogenation of mixtures of ethyne and ethene is studied. A heterogeneous model with axial dispersion of heat is solved numerically by means of a fully implicit discretisation scheme. From an analysis of the inlet and outlet boundary conditions, it follows that in order to avoid an influence of the type of boundary condition on the reactor behaviour, sufficiently long inert zones before and after the active bed should be present. Using preliminary kinetic expressions adapted from Mcn'shchikov ct al. (1975), the model calculations show a reasonable agreement with the experiments performed in a laboratory scale reactor and demonstrate the importance influence of small amounts of carbon monoxide both on the steady state as well as on the transient behaviour of the reactor. However, using the rate expressions derived from our own kinetic experiments in a Berty reactor, the behaviour under runaway conditions and the transition from non-runaway to runaway conditions can not be described well. Several factors that contribute to this discrepancy are discussed. This work shows that, in particular for a complex reaction system such as the selective hydrogenation of ethyne in ethene, the limited accuracy of the kinetic model and kinetic parameters dominates the precision attainable with packed bed reactor models.