Relativistic Keplerian orbital frequency and the related epicyclic frequencies play an important role in the physics of accretion discs orbiting Kerr black holes. We examine in detail their properties in Kerr spacetimes and discuss some possible observational implications resulting from their behaviour in the black hole case. Characteristics of the fundamental orbital frequencies of Keplerian motion are also analysed with the intention to find the phenomena which could observationally distinguisha hypothetical naked singularity from black holes. We explore the significant differences in behaviour of the epicyclic frequencies. These suggest that oscillations of discs orbiting Kerr black holes and naked singularities could be very different, and the information, given through X-ray variability of the source, could distinguish between the naked singularities and the black holes in general.