In this work we examine the standardized precipitation-evapotranspiration index (SPEI) as a tool for the assessment of climate in Croatia. The SPEI Index is based on water balance which is defined as a difference between rainfall and potential evapotranspiration in a location of interest. Unlike SPEI, the SPI Index depends only on precipitation. In order to model the water balance several three-parameter theoretical distributions are considered using the method of L-moments together with the Kolmogorov-Smirnov statistical test. The best fit is obtained for the log-normal distribution which is subsequently used to calculate the SPEI, while the usual gamma distribution is used for the SPI. Calculations are performed on timescales of 1, 3, 6 and 12 months for 31 main meteorological station in the Republic of Croatia. Detailed analysis is done for four representative stations belonging to four Croatian climatological regions: Osijek (Slavonija), Zagreb-Maksimir (central Croatia), Gospić (highland Croatia) and Split-Marjan (Dalmacija). Additionally, the droughts that occured in Croatia in 2003.-2004. and 2011.-2012. are analyzed by both indices for Zagreb-Maksimir station. It is shown that in some cases with considerable lack of rainfall the SPEI gives higher absolute values compared to the SPI, which is connected with higher surface air temperatures that significantly affect potential evapotranspiration, resulting in higher water demand. This points to advantages of SPEI over SPI as a measure of drought, both in a sense of intensity and duration. Moreover, these advantages could appear in greater importance over the next few decades due to global warming.