Global Navigation Satellite System (GNSS) observations play an important role in climate studies because of the advantages they provide. An analysis of the GNSS observations can be used to obtain the zenith total delay (ZTD) parameter, which represents the effect of weather conditions. In this study, the trends of the time series of IGS (International GNSS Service) Repro1 ZTD data recorded between 1995 and 2010 at 19 GNSS stations throughout Turkey and Europe reprocessed in the framework of COST Action ES1206 were investigated. The trends of the time series were estimated by using the Mann-Kendall rank correlation test in addition to Spearman's rho test and Sen's slope method. In addition, the Run (Swed-Eisenhart) test was performed to test for homogeneity. The aim of this study was to evaluate the advantages and disadvantages of the applications of different methods to the estimation of trends in the ZTD time series. According to the Mann-Kendall rank correlation test, the ANKR, GRAS, HERS and MAS1 stations exhibited an increasing trend. Using the Spearman rho test, increasing trends were observed at the ANKR, EBRE and MAS1 stations, while decreasing trends were observed at the BRUS and GRAS stations. Finally, negative slope values were obtained at the BRUS, GRAS, GRAZ, HERS, JOZE, PENC and WTZR stations by using the Sen slope method.