Changes in runoff parameters are very important for Slovakia, where stream-flow discharges, being supplied by precipitation and groundwater runoff, are preferentially influenced by climatic conditions. Therefore, teleconnections between runoff parameters, climate parameters and global atmospheric drivers such as North Atlantic Oscillation, Southern Pacific Oscillation, Quasi-biennial oscillation and solar activity were studied in the Nitra River Basin, Slovakia. Research was mostly based on records of 80 years (1931-2010) for discharges and baseflow, and 34 years for groundwater heads. Methods of autocorrelation, spectral analysis, cross-correlation and coherence function were used. Results of auto-correllograms for discharges, groundwater heads and base flow values showed a very distinct 11-year and 21-year periodicity. Spectrogram analysis documented the 11-year, 7.8-year, 3.6-year and 2.4-year periods in the discharge, precipitation and air temperature time series. The same cycles except of 11-years were also identified in the long-term series of the North Atlantic Oscillation and Southern Pacific Oscillation indices. The cycle from approximately 2.3 to 2.4-years is most likely connected with Quasi-biennial oscillation. The close negative correlation between the North Atlantic Oscillation winter index and the hydrological surface and groundwater parameters can be used for their prediction within the same year and also for one year in advance.