The late-time tails of massless and self-interacting (SI) (massive) scalar fields are investigated analytically in a stationary axisymmetric Einstein-Maxwell dilaton-axion (EMDA) black hole geometry. It is shown that the asymptotic behaviour of massless perturbations is dominated by an inverse power-law decaying tail and the intermediate asymptotic behaviour of SI (massive) perturbations is dominated by an oscillatory one.