This article illustrates the dynamic behaviour of the suspension of the bogie of the UAQ4 experimental superconducting levitating train. The levitation system uses high temperature (liquid nitrogen cooled) superconductor bulk materials on board and permanent magnets distributed on the guideway. The magnetic interaction between the two, and the Meissner effect, both lift and guide the vehicle. A model with one degree of freedom of the bogie is developed and parametric dynamic analyses are performed and discussed by varying the most significant system parameters.